# Surds And Indices Tips, Tricks And Shortcuts

## Surds and Indices Tips Tricks and Shortcuts

This page contains Tips, tricks and shortcuts of Surds and Indices along with its simplification and solved question and answers. ### Tips Tricks & 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
• 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

### Surds and Indices Formulas

• (a + b)(a – b) = (a2 – b2)
• (a + b)² = (a² + b² + 2ab)
• (a – b)² = (a² + b²- 2ab)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• (a³ + b³) = (a + b)(a² – ab + b²)
• (a³ – b³) = (a – b)(a²+ ab + b²)
• (a³ + b³ + c³ – 3abc) = (a + b + c)(a² + b² + c² – ab – bc – ac)
• When a + b + c = 0, then a³ + b³ + c³ = 3abc.

### Surds and Indices Rules

Rule NameSurds RuleIndices Rule
Multiplication Rulean * bn = (a*b)nan * am = a(m+n)
Division Rulean/ bn = (a/b)nam / an = a(m-n)
Power Rule(an)m = (a)nm
n√a = a(1/n)
a(nm)) = anm
a-n = 1/(an)

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### Type 1: Surds and Indices -Simplify the expression

Question . 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

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

Question . 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

### Type 3 : When base is same

Question : $If 5^{a} = 3125, then the value of 5^{(a – 3)} is$:

A. 25

B. 125

C. 625

D. 1625

Solution:

$5^{a} = 3125$

$5^{a} = 5^{5}$

a = 5.

$5^{(a – 3)} = 5^{(5 – 3)}$

$5^{2} = 25.$

Question : A person wants to know answer of question asked in annual exams as follows:$3^{0} + \frac{3^{-1}}{3^{-1}}- 3^{0}$ is simplified to

(1) –2
(2) –1
(3) 1
(4) 2

Solution :

Expression = $3^{0} + \frac{3^{-1}}{3^{-1}} – 3^{0}$

$\frac{1 +\frac{1}{3}}{\frac{1}{3} -1}$

$\frac{\frac{(3+1)}{3} }{\frac{(1-3)}{3}}$

$\frac{4}{3} \times -\frac{3}{2}$
= –2

Question : Simplify the equation $(256)^{0.16} × (4)^{0.36}$ is equal to

(1) 64
(2) 16
(3) 256.25
(4) 4

Solution :

$(256)^{0.16} \times (4)^{0.36}$

$(44)^{0.16} \times 4^{0.36}$

$4^{0.64} \times 4^{0.36}$

$(4)^{0.64 + 0.36} = 4$

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### One comment on “Surds And Indices Tips, Tricks And Shortcuts”

• manish

Very good lectures 2