# Surds and Indices practice test

1.

What is the value of (512)1/3 + (512)2/9 + (512)1/9 ?

Explanation:

(512)1/3 = (29)1/3 = 23 =8

(512)2/9 = (29)2/9 = 22 =4

(512)1/9 = (29)1/9  =2

= 8+4+2 = 14

2.

If x=5+2√6, then (x-1)/√x is equal to:

Explanation:

x=5+2√6=3+2+2√6=(√3)2+(√2)2+2*√3*√2=(√3+√2)2.
Also, (x-1)=4+2√6=2(2+√6)=2√2(√2+√3).
(x-1)/√x=2√2(√3+√2)/(√3+√2)=2√2.

3.

Find the value of [5[81/3+271/3]3]1/4

Explanation:

[5[(23)1/3+(33)1/3]3]1/4 [5[2+3]3]1/4

[54]1/4 => 5.
4.

[ (36)2 + (47)2 ] / ? = 28.04

Explanation:

(1296+2209) / ? =28.04

= 3505/? =28.04

? = 3505/28.05 = 125

5.

If x= ya , y = zb , z = xc then find the value of abc.

Explanation:

z= xc z= (ya)c [ x= ya ]

z= (y)ac
z= (zb)ac [y= zb]
z= zabc
abc = 1
6.

(25)7.5*(5)2.5/(125)1.5=5?

Explanation:

Let (25)7.5*(5)2.5/(125)1.5=5x. Then, [(52)7.5*(5)2.5]/(53)1.5=5x=[5(2*7.5)*52.5]/5(3*1.5)=5x

=[515*52.5]/54.5=5x=5x=5(15+2.5-4.5)=513=x=13.

7.

If m and n are whole numbers such that mn=121, then the value of (m-1)n+1 is:

Explanation:

We know that 112=121. Putting m=11 and n=2,We get:
(m-1)n+1=(11-1)(2+1)=103=1000

8.

If 3(x-y)=27 and 3(x+y)=243, then x is equal to:

Explanation:

3x-y=27=33=x-y=3…..(1)
3x+y=243=35=x+y=5….(2)
On solving (1) & (2), We get x=4

9.

The value of (8-25-8-26) is

Explanation:

( 8-25 – 8-26 ) => 8-26 (8-1 ) => 7* 8-26

10.

If (1/5)3y= 0.008 Then find the value of (0.25)y