How To Solve Surds And Indices Questions Quickly

How to Solve Surds and Indices Questions Quickly

The natural number which cannot be expressed in the  form of fraction known as Surds. For example: \sqrt{2} and the Indices refers to the power to which a number is raised. For example: 2²

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: \sqrt{2}
  • Indices: Indices refers to the power to which a number is raised. For example; 2²

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

Question 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 = \frac{1}{7^{25}} \frac{1}{7^{26}}

\frac{7 – 1}{7^{26}} = 6 × 7-26

Correct option: A

Question 2. Simplify (256) /mathbf{^ \frac{3}{4}}

Options:

A. 16

B. 12

C. 256

D. 64

Solution:    (256)^ \frac{3}{4} = (44)^ \frac{3}{4}= 43 = 64

Correct option: D

Question 3. Find the value of 8112 ÷ 8110

Options:

A. 72

B. 64

C. 81

D. 49

Solution:    We know,

\frac{a^m}{a^n} = am-n

= 8 (112 – 110) = 82 = 64

Correct option: B

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

Question 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 = \frac{80}{5}

4x = 16

 x = 2

 xx = 22 = 2

Correct option: D

Question 2. If 2a = 3 \sqrt{32}, then a is equal to:

Options:

A. \frac{1}{3}

B. 4

C. \frac{5}{3}

D. \frac{1}{2}

Solution:    Given value 2a

3 \sqrt{32}

2a = (32)^ \frac{1}{3}

2a = (25)^ \frac{1}{3}

2a = (2)^ \frac{1}{3}

a = \frac{5}{3}

Correct option: C

Question 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

Read Also Formulas to solve surds & indices questions 

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