Surds

Surds

by Aqil Mohammed

Multiple Choice

The following are considered as Surds except

• $$\sqrt{32}$$

• $$\sqrt{81}$$

• $$3\sqrt{5}$$

• $$\frac{1}{\sqrt{6}}$$

Multiple Choice

$$\sqrt{3}+\sqrt{3}=$$  

• $$\sqrt{6}$$  

• $$\sqrt{9}$$  

• $$2\sqrt{3}$$  

• $$3$$  

Multiple Choice

  $$\sqrt{3}\times\sqrt{4}$$ =

• $$\sqrt{3\times4}$$  

• $$\sqrt{3+4}$$  

• $$3\times4$$  

• $$\sqrt{7}$$  

Multiple Choice

$$\sqrt{6}\times\sqrt{6}\ \ne$$  

• $$\sqrt{36}$$  

• $$6$$  

• $$\left(\sqrt{6}\right)^2$$  

• $$6\sqrt{6}$$  

Multiple Choice

$$\frac{\sqrt{5}}{\sqrt{7}}=$$  

• $$\frac{5}{7}$$  

• $$\sqrt{\frac{5}{7}}$$  

• $$\sqrt{5}-\sqrt{7}$$  

• $$\left(\frac{5}{7}\right)^2$$  

Multiple Choice

Simplify the following surd...

• 3√2

• 2√3

• 9√2

• 3√6

Multiple Choice

Simplify the following surd...

• 6√2

• 2√6

• 8√2

• 4√6

Multiple Choice

Simplify the following surd...

• 4√2

• 2√3

• 6√2

• 4√3

Multiple Choice

Simplify

$$\sqrt{15}\times\sqrt{5}$$  

• $$\sqrt{75}$$  

• $$25\sqrt{3}$$  

• $$5\sqrt{3}$$  

• $$75$$  

Multiple Choice

Simplify

$$\sqrt{6}\times3\sqrt{6}$$  

• $$3\sqrt{36}$$  

• $$18\sqrt{6}$$  

• $$18$$  

• $$3$$  

Multiple Choice

Simplify

$$3\sqrt{7}+5\sqrt{7}$$  

• $$8\sqrt{14}$$  

• $$8\sqrt{7}$$  

• $$15\sqrt{14}$$  

• $$15\sqrt{7}$$  

Multiple Choice

Simplify

$$3\sqrt{3}+6\sqrt{7}-2\sqrt{7}+2\sqrt{3}$$  

• $$5\sqrt{3}+4\sqrt{7}$$  

• $$\sqrt{3}+4\sqrt{7}$$  

• $$9\sqrt{3}$$  

• $$5\sqrt{3}+8\sqrt{7}$$  

Multiple Choice

Simplify

$$\frac{4\sqrt{10}}{16\sqrt{2}}$$  

• $$\frac{\sqrt{5}}{2}$$  

• $$4\sqrt{5}$$  

• $$\frac{\sqrt{5}}{4}$$  

• $$\frac{5}{4}$$  

Multiple Choice

Expand

$$\sqrt{6}\left(2\sqrt{2}-6\right)$$  

• $$-2\sqrt{6}$$  

• $$-4\sqrt{6}$$  

• $$4\sqrt{2}-6\sqrt{6}$$  

• $$4\sqrt{3}-6\sqrt{6}$$  

Multiple Choice

Simplify

$$\frac{4\sqrt{2}\times5\sqrt{10}}{2\sqrt{5}}$$  

• $$20$$  

• $$40$$  

• $$10\sqrt{4}$$  

• $$\frac{20\sqrt{20}}{2\sqrt{5}}$$  

Multiple Choice

The equation is equal to

Multiple Choice

The equation is equal to

Multiple Choice

Multiple Choice

Rationalise its denominator

Multiple Choice

Fully simplify....

Multiple Choice

Fully simplify....

Multiple Choice

Fully simplify....

Multiple Choice

$$\left(\sqrt{2}-4\right)\left(\sqrt{2}+4\right)$$  

• 14

• $$-14$$  

• 2

• $$-2$$  

Multiple Choice

$$\left(\sqrt{7}+\sqrt{1}\right)\left(\sqrt{1}-\sqrt{7}\right)$$  

• 6

• $$-6$$  

• 8

• $$-8$$  

Multiple Choice

$$\left(\sqrt{3}-\sqrt{1}\right)\left(\sqrt{3}+\sqrt{1}\right)$$  

• $$-2$$  

• 2

• $$-4$$  

• 4

Multiple Choice

$$\left(\sqrt{s}-1\right)\left(1+\sqrt{s}\right)$$  

• $$\left(s-1\right)$$  

• $$\left(1-s\right)$$  

• $$\left(s^{2\ }-1\right)$$  

• $$\left(1-s^2\right)$$  

Multiple Choice

$$\left(x-\sqrt{2}\right)\left(\sqrt{2}+x\right)$$  

• $$\left(2-x\right)$$  

• $$\left(x-2\right)$$  

• $$\left(x^2-2\right)$$  

• $$\left(2-x^2\right)$$  

Multiple Choice

$$surds\ \ like\ \ a+\sqrt{b\ }\ and\ a-\sqrt{b}\ are\$$  

• $$like\ surds$$  

• $$unlike\ surds$$  

• $$conjugate\ surds$$  

• $$None$$  

Multiple Choice

The conjugate surd of $$\left(3-\sqrt{2}\right)$$  is

• $$\sqrt{2}-3$$  

• $$\sqrt{3}-\sqrt{2}$$  

• $$3+\sqrt{2}$$  

• $$\sqrt{3}-2$$  

Multiple Choice

$$conjugate\ surd\ of\ \ 5-\sqrt{3}\$$  

• $$5+\sqrt{3}$$  

• $$-\sqrt{3}$$  

• $$\sqrt{3}$$  

• $$-5$$  

Multiple Choice

$$conjugate\ term\ of\ 3+\sqrt{2}\ is$$  

• $$3$$  

• $$\sqrt{2}$$  

• $$3-\sqrt{2}$$  

• $$-\sqrt{2}$$  

Multiple Choice

Which of the following is considered as rationalising the denominator of   $$\frac{3-\sqrt{2}}{\sqrt{5}+4}$$  ?

• $$\frac{3-\sqrt{2}}{\sqrt{5}+4}\times\frac{3-\sqrt{2}}{\sqrt{5}-4}$$  

• $$\frac{3-\sqrt{2}}{\sqrt{5}+4}\times\frac{\sqrt{5}+4}{\sqrt{5}+4}$$  

• $$\frac{3-\sqrt{2}}{\sqrt{5}+4}\times\frac{4-\sqrt{5}}{4-\sqrt{5}}$$  

• $$\frac{3-\sqrt{2}}{\sqrt{5}+4}\times\frac{\sqrt{5}-4}{\sqrt{5}-4}$$  

Multiple Choice

What should you multiply $$\frac{6}{1-\sqrt{5}}$$  by to rationalize the denominator?

• -4

• $$1-\sqrt{5}$$  

• $$1+\sqrt{5}$$  

• $$-\frac{\left(3-3\sqrt{5}\right)}{2}$$  

Multiple Choice

$$\frac{-2}{1+\sqrt{6}}$$  Rationalize the following:

• $$\frac{1+\sqrt{6}}{-2}$$  

• $$\frac{-2+2\sqrt{6}}{-5}$$  

• $$-\frac{2\sqrt{6}}{6}$$  

• $$-2\sqrt{6}$$  

Multiple Choice

Rationalize the following: $$\frac{\sqrt{2}}{\sqrt{3}+\sqrt{5}}$$  

• $$\frac{\sqrt{6}-\sqrt{10}}{8}$$  

• $$\frac{\sqrt{6}-\sqrt{10}}{-2}$$  

• $$\frac{\sqrt{6}+\sqrt{10}}{8}$$  

• $$\frac{2\sqrt{3}+2\sqrt{5}}{-2}$$  

Open Ended

Leave your feedback on this topic

Extension Surd Problems​

​(Algebraic)

Multiple Choice

Solve

$$\sqrt{x-3}=2$$  

• 4

• 5

• 6

• 7

Multiple Choice

Solve

$$\sqrt{2x+1}=\sqrt{1-x}$$  

• 0

• 1

• 2

• 3

Multiple Choice

Solve

$$3\sqrt{1-x}=x+3$$  

• -15

• -6

• 0

• 5

Multiple Select

Solve

$$\sqrt{2x^2-5x-3}=\sqrt{3x-3}$$  

• 0

• 2

• 4

• 6

Multiple Select

Solve

$$\sqrt{x-4}-\sqrt{x-3}=-1$$  

• 0

• 2

• 4

• 6

Multiple Select

Solve

$$1+\sqrt{x+3}=\sqrt{2x-1}$$  

• 1

• 5

• 7

• 13

Multiple Choice

Solve

$$\sqrt{x+1}=3-\sqrt{x}$$  

• $$\frac{4}{3}$$  

• 2

• 3

• $$\frac{16}{9}$$