CBSE Class 9 Mental Maths Number System Worksheet

Question. Simplify 4√32
Answer : 2 ⁴√2

Question. Which is greater 3√3 and 4√5 ?
Answer : ⁴√5

Question. Write in ascending form 3√4, 3√2, 3√3 ?
Answer : ³√2, ³√3, ³√4

Question. Simplify √8 + √32 − √2
Answer : ⁵√2

Question. Multiply 3√7 by √2
Answer : ⁶√392

Question. Divide √24 by 3√200
Answer : ⁶√216/625

Question. What is value of (8^3/5)5 ?
Answer : 512

Question. What is value of 4^1/5 8^1/5 ?
Answer : 2

Question. What is value of 8^1/5 ÷8^1/3 ?
Answer : 8-2/15 or 2^-2/5

Question. Simplify 63 x (1/2)3
Answer : 27

Question. What is pure surd of 3/4√32 ?
Answer : √18

Question. Write into simplest form 5√3125
Answer : 5

Question. Simplify 4√3+ 27
Answer : 7√3

Question. Find two rational numbers between 1/2 and 1/4
Answer : 3/8, 7/16

Question. Find the two rational numbers between -1 and 3/2
Answer : –15/16 , 23/16

Question. Find three rational numbers -5 and 3/4
Answer : −17/8. −57/16, −45/32

Question. Find four rational numbers between -1 and 1
Answer : 0, -1/2, 1/2 , 3/4

Question. Express .37 in the form of p/q .
Answer : 37/99

Question. Express .54in the form of p/q .
Answer : 6/11

Question. Express 3.14 in the form of p/q .
Answer : 311/99

Question. What is the correct approximate decimal representation of √3 upto two decimals.
Answer : 1.73

Question. Express ³√−108a⁴b³ in the simplest form
Answer : –3ab³√4a

Question. Express ⁴√a⁸b⁶c⁷ in th simplest form.
Answer : a²bc⁴√b²c³

Question. What is the decimal representation of 3(3/8) .
Answer : 3.375

Question. What is the decimal representation of 5/6 .
Answer : 0.83

Question. Give the decimal representation of 327/500 .
Answer : 1.154

Question. Find three rational numbers between 0 and 1/10 .
Answer : 1/40, 1/20, 3/40

Question. What is the rational denominator of 1/√3+ √2
Answer : √3 - √2

Question. If 3 = 1.732, what is the value of 2/√3 .
Answer : 1.154

Question. Express 4/√5−1 with rational denominator.
Answer : √5 +1

Question. Express 10/√7−√5 with rational denominator.
Answer : 5(√7 + √5)

Question. Express  16/√41−5 with a rational denominator.
Answer : √41 + 5

Question. Find the value of (512)^-2/9
Answer : 1/4

Question. Find the value of (125)^2/9
Answer : ³√25

Question. If x = √2+1, find the value of (x - 1/x)²
Answer : 4

Question. Which of the following is rational or irrational number.
(i) (2 + √3)²
(ii) (3 + √4)²
Answer : Irrational, rational

Question. If P = 3−2√2, what is the value of P² + 1/P²
Answer : 34

Question. Express as a pure Surd: 2xy ³√xy .
Answer : 3√8x⁴ y⁴

Question. Express as pure surd : a^{1/2 3}√ab² .
Answer : 3√a^5/2 √b²

Question. Find the value of 4√12×7√6
Answer : 168√2

Question. Simplify √27/80 .
Answer : 3/20 √15

Question. Find the value of 1/√10 when √10 = 3.162 .
Answer : 0.316

Question. If x =7+4 3 , what is the value of √x + 1/√x .
Answer : 4

Question. Find three rational numbers between 0 and 1.
Answer : 1/4, 1/2, 3/4

Question. What is the value of 2 + √3 / 2 - √3
Answer : 7 + 4√3

Question. What is the value of 1/3 + √2 ?
Answer : 3 + √2 / 7

Question. Find the value of √8 × √50 .
Answer : 20

Question. If 2 =1.41, find the value of 1/√2 .
Answer : .705

Question. Divide √162 by √2 .
Answer : 9

Question. Find the rationalising factor of ³√49 .
Answer : ³√7

Question. What is the value of 7√6 524.
Answer : 420

Question. If √3 =1.732, what is the value of 5/√3 ?
Answer : 2.886

Question. If ³√2 = (x)^1/2 , what is the value of x?
Answer : ³√4

Question. If (⁴√49) = x^1/2 , what is the value of x?
Answer : 7

Question. What is the value of 3√5 2√3 3√5 2√3 ?
Answer : 33