Tips And Tricks And Shortcuts for Surds and Indices

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