Free Printable Surds

1.

$Solve\ 2^{2x}\times3^x=144$

a)

x=1

b)

x=2

c)

x=3

d)

x=4

2.

Express $\frac{-8+4\ \sqrt[\ ]{3}}{4+2\ \sqrt[]{3}}\ in\ the\ form\ of\ a+b\ \sqrt[\ ]{3}$ , where a and b are integers

a)

$14+8\ \sqrt[]{3}$

b)

$14-8\ \sqrt[]{3}$

c)

$-14+8\ \sqrt[]{3}$

d)

$-14-8\ \sqrt[]{3}$

3.

The area of a right-angled triangle is 18 cm² . If its height is $7-\sqrt[]{13}$ cm, find the length of its base.

a)

$\frac{7}{2}-\frac{1}{2}\ \sqrt[]{13}$

b)

$\frac{7}{2}+\frac{1}{2}\ \sqrt[]{13}$

c)

$7-\sqrt[]{13}$

d)

$7+\sqrt[]{13}$

4.

Given that $\frac{72x^{\frac{2}{3}}}{\left(6x^{-3}\right)^3}=3^ax^b,\ find\ the\ value\ of\ a\ and\ b$

a)

$1,\ \frac{29}{3}$

b)

$-1,\frac{29}{3}$

c)

$1,-\frac{29}{3}$

d)

$-1,-\frac{29}{3}$

5.

Solve the simultaneous equation $2^x\times2^y=16,\ 3^{2x}\ \div\ \left(\frac{1}{3}\right)^{\left(y-1\right)}=81$

a)

x=1 y=3

b)

x=3 y=1

c)

x=-1 y=3

d)

x=1 y=-3

6.

Without using a calculator, express $6\left(1+\sqrt[]{3}\right)^{-2}\ in\ the\ form\ of\ a+b\ \sqrt[]{3},\ find\ integers\ a\ and\ b$

a)

a=6, b=3

b)

a=-6, b=3

c)

a=-6, b=-3

d)

a=6, b=-3

7.

Solve the equation $\sqrt[]{x+1}\ +\ \sqrt[]{2x+3}\ =\ 5$

(a)

8.

Given that $\sqrt[]{6-4\ \sqrt[]{2}}=\sqrt[]{a}-\sqrt[]{b}$ , find the value of a and b

a)

a=4, b=2

b)

a=8, b=4

c)

a=2, b=4

d)

a=2, b= $\sqrt[]{2}$

Surds

Total questions: 8

Worksheet time: 27mins

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