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

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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Geometry of Spirals

Why is it useful to rationalise the denominator?

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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