Look at the right-angled triangle on card A. Work out each of the quantities on the other cards and give your answers in simplified surd form. E. Determine the dimensions of the smallest triangle, similar to ABC, only one of whose side lengths is not an integer.

The smallest triangle has dimensions 1, √3, 2

The smallest triangle has dimensions 2, √3, 3

The smallest triangle has dimensions 3, √3, 4

The smallest triangle has dimensions 1, √2, √3

Simplify the expression $$\frac{2\sqrt{3}}{3}$$ .

Simplified expression is $$\frac{2\sqrt{3}}{3}$$ .

Simplified expression is $$\frac{\sqrt{3}}{3}$$ .

Simplified expression is $$\frac{2}{3}$$ .

Simplified expression is $$\sqrt{3}$$ .

What is the result of $$\sqrt{80}$$ ?

The result of $$\sqrt{80}$$ is $$4\sqrt{5}$$ or approximately 8.944.

The result of $$\sqrt{80}$$ is $$5\sqrt{4}$$ or approximately 9.165.

The result of $$\sqrt{80}$$ is $$3\sqrt{6}$$ or approximately 8.485.

The result of $$\sqrt{80}$$ is $$2\sqrt{10}$$ or approximately 8.944.

Find the value of $$\frac{1}{\sqrt{5} - \sqrt{3}}$$ .

The value of $$\frac{1}{\sqrt{5} - \sqrt{3}}$$ is $$\frac{\sqrt{5} + \sqrt{3}}{2}$$ .

The value of $$\frac{1}{\sqrt{5} - \sqrt{3}}$$ is $$\sqrt{5} - \sqrt{3}$$ .

The value of $$\frac{1}{\sqrt{5} - \sqrt{3}}$$ is $$\frac{2}{\sqrt{5} + \sqrt{3}}$$ .

The value of $$\frac{1}{\sqrt{5} - \sqrt{3}}$$ is $$\sqrt{5} + \sqrt{3}$$ .

What is the value of $$\frac{\sqrt{54}}{\sqrt{6}}$$ ?

The value of $$\frac{\sqrt{54}}{\sqrt{6}}$$ is 3.

The value of $$\frac{\sqrt{54}}{\sqrt{6}}$$ is 2.

The value of $$\frac{\sqrt{54}}{\sqrt{6}}$$ is 4.

The value of $$\frac{\sqrt{54}}{\sqrt{6}}$$ is 5.

Simplify $$\frac{3}{\sqrt{3}}$$ .

Simplified form is $$\sqrt{3}$$ .

Simplified form is $$\frac{3\sqrt{3}}{3}$$ .

Simplified form is $$\frac{3}{3}$$ .

What is the result of $$\sqrt{2}$$ ?

The result of $$\sqrt{2}$$ is approximately 1.414.

The result of $$\sqrt{2}$$ is approximately 1.5.

The result of $$\sqrt{2}$$ is approximately 1.7.

The result of $$\sqrt{2}$$ is approximately 1.2.

Find the value of $$\frac{1}{\sqrt{5} + \sqrt{3}}$$ .

The value of $$\frac{1}{\sqrt{5} + \sqrt{3}}$$ is $$\frac{\sqrt{5} - \sqrt{3}}{2}$$ .

The value of $$\frac{1}{\sqrt{5} + \sqrt{3}}$$ is $$\frac{\sqrt{5} + \sqrt{3}}{2}$$ .

The value of $$\frac{1}{\sqrt{5} + \sqrt{3}}$$ is $$\frac{2}{\sqrt{5} - \sqrt{3}}$$ .

The value of $$\frac{1}{\sqrt{5} + \sqrt{3}}$$ is $$\frac{2}{\sqrt{5} + \sqrt{3}}$$ .

Calculate the value of $$5 + 2\sqrt{6}$$ .

The value of $$5 + 2\sqrt{6}$$ is approximately 9.898.

The value of $$5 + 2\sqrt{6}$$ is approximately 7.000.

The value of $$5 + 2\sqrt{6}$$ is approximately 10.000.

The value of $$5 + 2\sqrt{6}$$ is approximately 8.500.

What is the result of $$\sqrt{8}$$ ?

The result of $$\sqrt{8}$$ is $$2\sqrt{2}$$ or approximately 2.828.

The result of $$\sqrt{8}$$ is $$3\sqrt{2}$$ or approximately 3.464.

The result of $$\sqrt{8}$$ is $$4\sqrt{2}$$ or approximately 5.656.

The result of $$\sqrt{8}$$ is $$5\sqrt{2}$$ or approximately 7.071.

What is the simplified form of $$\frac{\sqrt{5} + \sqrt{3}}{2}$$ ?

The simplified form of $$\frac{\sqrt{5} + \sqrt{3}}{2}$$ is $$\frac{1}{2}(\sqrt{5} + \sqrt{3})$$ .

The simplified form of $$\frac{\sqrt{5} + \sqrt{3}}{2}$$ is $$\sqrt{5} + \sqrt{3}$$ .

The simplified form of $$\frac{\sqrt{5} + \sqrt{3}}{2}$$ is $$\frac{\sqrt{5} - \sqrt{3}}{2}$$ .

The simplified form of $$\frac{\sqrt{5} + \sqrt{3}}{2}$$ is $$\frac{\sqrt{5} + \sqrt{3}}{4}$$ .

What is the result of $$2\sqrt{5} \times 4\sqrt{5}$$ ?

The result of $$2\sqrt{5} \times 4\sqrt{5}$$ is $$40$$ .

The result of $$2\sqrt{5} \times 4\sqrt{5}$$ is $$20$$ .

The result of $$2\sqrt{5} \times 4\sqrt{5}$$ is $$10$$ .

The result of $$2\sqrt{5} \times 4\sqrt{5}$$ is $$50$$ .

What is the value of $$3\sqrt{2} \times 4\sqrt{3}$$ ?

The value of $$3\sqrt{2} \times 4\sqrt{3}$$ is $$12\sqrt{6}$$ .

The value of $$3\sqrt{2} \times 4\sqrt{3}$$ is $$7\sqrt{5}$$ .

The value of $$3\sqrt{2} \times 4\sqrt{3}$$ is $$6\sqrt{12}$$ .

The value of $$3\sqrt{2} \times 4\sqrt{3}$$ is $$9\sqrt{8}$$ .

What is the result of $$(\sqrt{3} + \sqrt{2})^2$$ ?

The result of $$(\sqrt{3} + \sqrt{2})^2$$ is $$3 + 2 + 2\sqrt{6}$$ = $$5 + 2\sqrt{6}$$ .

The result of $$(\sqrt{3} + \sqrt{2})^2$$ is $$3 + 2 - 2\sqrt{6}$$ = $$5 - 2\sqrt{6}$$ .

The result of $$(\sqrt{3} + \sqrt{2})^2$$ is $$3 - 2 + 2\sqrt{6}$$ = $$1 + 2\sqrt{6}$$ .

The result of $$(\sqrt{3} + \sqrt{2})^2$$ is $$3 + 2 + \sqrt{6}$$ = $$5 + \sqrt{6}$$ .

What is the value of $$\sqrt{8} \times \sqrt{50}$$ ?

The value of $$\sqrt{8} \times \sqrt{50}$$ is $$20$$ .

The value of $$\sqrt{8} \times \sqrt{50}$$ is $$30$$ .

The value of $$\sqrt{8} \times \sqrt{50}$$ is $$40$$ .

The value of $$\sqrt{8} \times \sqrt{50}$$ is $$\sqrt{50}$$ .

What is the value of $$2\sqrt{2}$$ ?

The value of $$2\sqrt{2}$$ is approximately 2.828.

The value of $$2\sqrt{2}$$ is approximately 3.5.

The value of $$2\sqrt{2}$$ is approximately 4.

The value of $$2\sqrt{2}$$ is approximately 2.

Simplify the expression $$\sqrt{48}$$ .

The simplified form of $$\sqrt{48}$$ is $$4\sqrt{3}$$ .

The simplified form of $$\sqrt{48}$$ is $$2\sqrt{12}$$ .

The simplified form of $$\sqrt{48}$$ is $$8\sqrt{6}$$ .

The simplified form of $$\sqrt{48}$$ is $$3\sqrt{16}$$ .

Simplify the expression $$\frac{1}{\sqrt{2} - 1}$$ .

Simplified expression is $$\sqrt{2} + 1$$ .

Simplified expression is $$\sqrt{2} - 1$$ .

Simplified expression is $$2 + \sqrt{2}$$ .

Simplified expression is $$2 - \sqrt{2}$$ .

Simplify the expression $$\sqrt{8 \div \sqrt{2}}$$ .

The simplified expression is $ 4 $.

The simplified expression is $ 2 $.

The simplified expression is $$\sqrt{4}$$ .

The simplified expression is $$\sqrt{8}$$ .

Simplify the expression $$\sqrt{2}(\sqrt{8} + \sqrt{2})$$ .

Simplified expression is $$4\sqrt{2}$$ .

Simplified expression is $$2\sqrt{10}$$ .

Simplified expression is $$2\sqrt{6}$$ .

Simplify the expression $$x \div \sqrt{x}$$ .

Simplified expression is $$\sqrt{x}$$ .

Simplified expression is $$x^2$$ .

Simplified expression is $ x $.

Simplified expression is $$\frac{1}{x}$$ .

Simplify the expression $$\frac{3\sqrt{2} \times 4\sqrt{3}}{4\sqrt{3}}$$ .

Simplified expression is 3√2.

Simplified expression is 4√3.

Simplified expression is 3√3.

Simplified expression is 2√2.

Simplify the expression: $$\sqrt{54}$$ .

Simplified expression is $$3\sqrt{6}$$ .

Simplified expression is $$6\sqrt{3}$$ .

Simplified expression is $$2\sqrt{27}$$ .

Simplified expression is $$9\sqrt{2}$$ .

Simplify the expression: $$\frac{10}{\sqrt{5}}$$ .

Simplified expression is $$2\sqrt{5}$$ .

Simplified expression is $$\frac{10\sqrt{5}}{5}$$ .

Simplified expression is $$\frac{2}{\sqrt{5}}$$ .

Simplified expression is $$\frac{5}{\sqrt{2}}$$ .

Simplify the expression: $$\frac{\sqrt{x^6}}{x}$$ .

Simplified expression is $$x^{2.5}$$ or $$\frac{x^3}{\sqrt{x}}$$ .

Simplified expression is $$x^{3}$$ or $$\sqrt{x^6}$$ .

Simplified expression is $$x^{2}$$ or $$\frac{x^4}{x^2}$$ .

Simplified expression is $$x^{1.5}$$ or $$\frac{x^3}{x}$$ .

Simplify the expression: $$\frac{3}{\sqrt{3}}$$ .

Simplified expression is $$\sqrt{3}$$ .

Simplified expression is $ 3 $.

Simplified expression is $$\frac{1}{\sqrt{3}}$$ .

Simplified expression is $$\frac{3\sqrt{3}}{3}$$ .

Geometry of Spirals

Authored by selena issur

Mathematics

10th Grade

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify $\sqrt{72}$ .

$6\sqrt{2}$

$8\sqrt{3}$

$4\sqrt{6}$

$3\sqrt{8}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Expand $3\sqrt{2}(5-\sqrt{2})$ .

$15\sqrt{2}$ - 6.

$15\sqrt{2} - 3\sqrt{2}$

$3\sqrt{2} - 5\sqrt{2}$

15 - $3\sqrt{2}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Rationalise the denominator of $\frac{6}{5\sqrt{2}}$ .

$\frac{6\sqrt{2}}{10}$

$\frac{6\sqrt{2}}{5}$

$\frac{6}{5}$

$\frac{6}{10}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify $\left( 4\sqrt{2} \times \frac{1}{16} \times \sqrt{32} \right)^2$ .

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why is it useful to rationalise the denominator?

To make the expression easier to work with by eliminating radicals from the denominator.

To increase the complexity of the expression.

To convert the expression into a fraction.

To change the sign of the numerator.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify the expression: $\cos 45^\circ = \frac{1}{\sqrt{2}} = ?$ .

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{2}}{2}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-8 \pm \sqrt{8^2 - 4}}{2} = ?$ .

x = $\frac{-8 \pm \sqrt{60}}{2}$

x = $\frac{-8 \pm \sqrt{60}}{4}$

x = $\frac{-8 \pm \sqrt{60}}{8}$

x = $\frac{-8 \pm \sqrt{60}}{16}$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Simplify the expression for the length of a line in coordinate geometry: $\sqrt{6^2 + 9^2} = ?$ .

$\sqrt{117}$

$15$

$10.82$

$11.18$

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Geometry of Spirals

Simplify $\sqrt{72}$ .

Expand $3\sqrt{2}(5-\sqrt{2})$ .

Rationalise the denominator of $\frac{6}{5\sqrt{2}}$ .

Simplify $\left( 4\sqrt{2} \times \frac{1}{16} \times \sqrt{32} \right)^2$ .

Why is it useful to rationalise the denominator?

Simplify the expression: $\cos 45^\circ = \frac{1}{\sqrt{2}} = ?$ .

Simplify the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-8 \pm \sqrt{8^2 - 4}}{2} = ?$ .

Simplify the expression for the length of a line in coordinate geometry: $\sqrt{6^2 + 9^2} = ?$ .

Look at the right-angled triangle on card A. Work out each of the quantities on the other cards and give your answers in simplified surd form. A. Calculate the length of AC in metres.

Look at the right-angled triangle on card A. Work out each of the quantities on the other cards and give your answers in simplified surd form. B. Calculate the length of AC.

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Similar Resources on Wayground

Popular Resources on Wayground

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Geometry of Spirals

Simplify 72\sqrt{72}72​ .

Expand 32(5−2)3\sqrt{2}(5-\sqrt{2})32​(5−2​) .

Rationalise the denominator of 652\frac{6}{5\sqrt{2}}52​6​ .

Simplify (42×116×32)2\left( 4\sqrt{2} \times \frac{1}{16} \times \sqrt{32} \right)^2(42​×161​×32​)2 .

Why is it useful to rationalise the denominator?

Simplify the expression: cos⁡45∘=12=?\cos 45^\circ = \frac{1}{\sqrt{2}} = ?cos45∘=2​1​=? .

Simplify the quadratic formula: x=−b±b2−4ac2a=−8±82−42=?x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-8 \pm \sqrt{8^2 - 4}}{2} = ?x=2a−b±b2−4ac​​=2−8±82−4​​=? .

Simplify the expression for the length of a line in coordinate geometry: 62+92=?\sqrt{6^2 + 9^2} = ?62+92​=? .

Look at the right-angled triangle on card A. Work out each of the quantities on the other cards and give your answers in simplified surd form. A. Calculate the length of AC in metres.

Look at the right-angled triangle on card A. Work out each of the quantities on the other cards and give your answers in simplified surd form. B. Calculate the length of AC.

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Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Simplify $\sqrt{72}$ .

Expand $3\sqrt{2}(5-\sqrt{2})$ .

Rationalise the denominator of $\frac{6}{5\sqrt{2}}$ .

Simplify $\left( 4\sqrt{2} \times \frac{1}{16} \times \sqrt{32} \right)^2$ .

Simplify the expression: $\cos 45^\circ = \frac{1}{\sqrt{2}} = ?$ .

Simplify the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-8 \pm \sqrt{8^2 - 4}}{2} = ?$ .

Simplify the expression for the length of a line in coordinate geometry: $\sqrt{6^2 + 9^2} = ?$ .