How To Solve Surds And Indices Questions Quickly

How to Solve Surds and Indices Ques. Quickly :

Surds: Number which cannot be expressed in the fraction form of two integers is called as surd. For example; √2

Indices: Indices refers to the power to which a number is raised. For example; 2²

How to solve Surds and Indices quickly

Type 1: How to Solve Surds and Indices Quickly- Simplify the expression

Ques 1.

Find the value of 7-25 – 7-26
Options:
A. 6 * 7-26
B. 6 * 7-25
C. 7 * 7-25
D. 7 * 7-26

Solution:

7-25 – 7-26 = 1/725 – 1/726
= (7-1)/726 = 6 * 7-26

Correct option: a

Ques 2.

Simplify (256)3/4
Options:
A. 16
B. 12
C. 256
D. 64

Solution:

(256)3/4 = (44)3/4 = 43 = 64

Correct option: D

Ques 3.

Find the value of 8112 ÷ 8110

Options:
A. 72
B. 64
C. 81
D. 49

Solution:

We know,

am/a= am-n
= 8 (112 – 110) = 82 = 64

Correct option: B

Type 2: Solve Surds and Indices Quickly- Find the value of x

Ques 1.

If 4x + 4x + 1 = 80, then the value of xx  is
Options:
A. 16
B. 9
C. 25
D. 4

Solution:

4x(1 + 4) = 80

= 4x  * 5 = 80

= 4x = 80/5
= 4x = 16

= x = 2
 xx = 22 = 2

Correct option: D

Ques 2.

If 2a = 3√32, then a is equal to:
Options:
A. 1/3
B. 4
C. 5/3
D. 1/2

Solution:

Given value 2a = 3√32
= 2a = (32)1/3
= 2a = (25)1/3
= 2a = (2)5/3
a = 5/3

Correct option: C

Ques 3.

If x and y are whole numbers such that xy = 169, then find the value of (x – 1)y + 1
Options:
A. 1331
B. 2744
C. 1728
D. 729

Solution:

169 = 132
So, the value of x = 13 and y = 2
Now, (x – 1)y + 1
= (13 – 1)2+1
= (12)

=1728

Correct option: C

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