Quantitative aptitude SURDS & INDICES for Bank PO / Clerk Preparation

Quantitative aptitude for Bank PO / Clerk Preparation – SURDS & INDICES

Baking Online Classes : Surds & Indices is one of the important chapters from which you can expect questions in banking as well as SSC level exams. The concept of surds & indices is very easy but you have to practice as much as questions you can so that you can solve the problems in the exams easily.

Laws of Indices:

• a^m x aⁿ = a^{m + n}
• a^m / aⁿ = a^m-n
• (a^m)ⁿ = a^mn
• (ab)ⁿ = aⁿbⁿ
• (a/b)ⁿ = aⁿ / bⁿ
• a⁰ = 1

Surds:

Let a be a rational number and n be a positive integer such that a^(1/n) = , then

• = a^(1/n)
• =
• /b =
• ()ⁿ= a

Ques: 1 (15)^3.5x (15)^?= 15⁸

Sol: Let (15)^3.5x (15)^x= 15⁸.

Then, (15)^{3.5 + x}= 15⁸.

So, 3.5 + x = 8

x= (8 – 3.5)

x= 4.5

 Ques: 2If 5^a= 3125, then the value of 5^{(a – 3)} is:

Sol: As 5^a= 3125 → 5^a= 5⁵

So, a = 5.

5^{(a – 3)} = 5^{(5 – 3)} = 5² = 25.

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Ques: 3 (256)^0.16 x (256)^0.09 =?

Sol: (256)^0.16 x (256)^0.09 = (256^{)(0.16 + 0.09)}

= (256)^0.25

= (256)^(25/100)

= (256)^(1/4)= (4⁴)(1/4)

= 4¹= 4

Ques: 4 The value of [(5)¹⁵⁰÷ (5)¹⁴⁶]

Sol: (5)¹⁵⁰÷ (5)¹⁴⁶= 5^(150-146)

= 5⁴

= 625 

Ques 5: If 3^{(x – y)} = 27 and 3^{(x + y)} = 243, then y is equal to:

Sol: 3^{x – y} = 27 = 3³

So, x – y = 3 ….(i)

Also, 3^{x + y} = 243 = 3⁵

So, x + y = 5…. (ii)

On solving (i) and (ii),

we get x = 4.

So, y= 1

Ques: 6 If (a/b)^{x – 1}=(b/ a)^{x – 3}, then the value of x is:

Sol: Given (a/b)^{x – 1}=(b/ a)^{x – 3}

Then, (a/b)^{x – 1}=(a/ b)^{–(x – 3)}

So, x – 1 = 3 – x

2x = 4

x = 2.

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