Tips And Tricks And Shortcuts For Surds And Indices

August 4, 2020

Tips and Tricks and Shortcuts For Surds and Indices

Surds: Numbers which can be expressed in the form $\sqrt{p} + \sqrt{q}$ , where p and q are natural numbers and not perfect squares.
Indices: Indices refers to the power to which a number is raised. For example: 3²

Surds: Numbers which can be expressed in the form $\sqrt{p} + \sqrt{q}$ , where p and q are natural numbers and not perfect squares.
Indices: Indices refers to the power to which a number is raised. For example; 32
Here, are quick and easy tips and tricks for you to solve Surds and Indices Formulas with Power questions quickly, easily, and efficiently in competitive exams and other recruitment exams .
Memorize all square and cube value from numbers 1 – 20 to solve the questions fast.

Question 1. Find the value (1728)^{( $– \frac{2}{3}$ )}

Options.

A. $\frac{1}{144}$

B. 144

C. – $\frac{1}{144}$

D. $\frac{1}{12}$

Solution: Cube root of 1728 is 12.

Therefore,(12)^{–3( $\frac{1}{3}$ )}

(12) ^{– 3 × ( $\frac{2}{3}$ )} = 12^–2

We know that, a^-n = ^{$\frac{1}{a}^n$}

Therefore, 12^–2 = $(\frac{1}{12})^2$ = $\frac{1}{144}$

Correct option: A

Question 1. Find the value of x If ( $\frac{p}{q}$ )^x-1= ( $\frac{q}{p}$ )^x-3

Options.

A. 3

B. 2

C. 1

D. -2

Solution: ( $\frac{p}{q}$ )^x-1= ( $\frac{q}{p}$ )^x-3

( $\frac{p}{q}$ )^x-1= ( $\frac{p}{q}$ )^-(x-3)

( $\frac{p}{q}$ )^x-1= ( $\frac{p}{q}$ )^3-x

x-1 = 3-x

x = 2

Correct option: B

Read Also –Formulas for Surds and Indices