Find the value of the following: 1125 × 1944 3

We need to find, the value of 1125 × 1944 3 Then, 1125 × 1944 3 = 1125 3 × 1944 3 By prime factorisation, we get, 5 1125 5 225 5 45 3 9 3 3 1 2 1944 2 972 2 486 3 243 3 81 3 27 3 9 3 3 1 ∴ 1125 × 1944 3 = 5 × 5 × 5 × 3 × 3 3 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 3 = 5 × 2 × 3 × 3 3 × 3 3 = 90 3 3 Hence, 1125 × 1944 3 = 90 3 3

Find the value of the following: 274 . 625 3

We need to find, the value of 274 . 625 3 Then, 274 . 625 3 = 274625 1000 3 = 274625 3 1000 3 Now, by prime factorisation we get, 5 274625 5 54925 5 10985 13 2197 13 169 13 13 1 2 1000 2 500 2 250 5 125 5 25 5 5 1 ∴ 274 . 625 3 = 274625 3 1000 3 = 5 × 5 × 5 × 13 × 13 × 13 3 2 × 2 × 2 × 5 × 5 × 5 3 = 5 × 13 3 3 5 × 2 3 3 = 65 10 = 6 . 5 Hence, 274625 3 = 6 . 5

Find the value of the following: 5832 6859 3

We need to find, the value of 5832 6859 3 Then, 5832 6859 3 = 5832 3 6859 3 Now, by prime factorisation we get, 2 5832 2 2916 2 1458 3 729 3 243 3 81 3 27 3 9 3 3 1 19 6859 19 361 19 19 1 ∴ 5832 6859 3 = 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 3 19 × 19 × 19 3 = 2 × 3 × 3 3 3 19 3 3 = 18 19 Hence, 5832 6859 3 = 18 19

E M B I B E

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 6

MEDIUM

8th CBSE

IMPORTANT

Earn 100

Find the cube root of the following number by using prime factorisation.

$15625$

Important Questions on Square and Square Root; Cube and Cube Root

HARD

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 7

Find the value of the following:

$\sqrt[3]{125 \times 64}$

HARD

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 7

Find the value of the following:

$\sqrt[3]{1125 \times 1944}$

HARD

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 7

Find the value of the following:

$\sqrt[3]{274.625}$

HARD

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 7

Find the value of the following:

$\sqrt[3]{\frac{5832}{6859}}$

MEDIUM

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 8

Find the volume of a cube if each of its side measures $5.2 cm$ .

HARD

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 9

Find the smallest number by which $2025$ must be multiplied to make it a perfect cube. Also find the cube root of the number thus obtained.

HARD

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 10

Find the smallest number by which $140625$ must be divided, so that the quotient thus obtained is a perfect cube. Also find the cube root of the number thus obtained.

MEDIUM

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.5>Q 11

Find the edge of a cube whose volume is $166.375 {cm}^{3}$ .