If 3969 = 63 , then find the value of 0 . 003969 .

Given that 3969 = 63 , to find the value of 0 . 003969 . We have 0 . 003969 = 3969 1000000 = 3969 100 × 100 × 100 3969 100 × 100 × 100 = 3969 10 2 × 10 2 × 10 2 Now, 3969 10 2 × 10 2 × 10 2 = 63 10 × 10 × 10 = 63 1000 Therefore, 0 . 003969 = 0 . 063

If 3969 = 63 , then find the value of 39 . 69 .

Given that 3969 = 63 , to find the value of 39 . 69 . We have 39 . 69 = 3969 100 = 3969 10 2 Now, 3969 10 2 = 63 10 Therefore, 39 . 69 = 6 . 3

If 3969 = 63 , then find the value of 0 . 3969 .

Given that 3969 = 63 , to find the value of 0 . 3969 . We have 0 . 3969 = 3969 10000 = 3969 100 × 100 3969 100 × 100 = 3969 10 2 × 10 2 Now, 3969 10 2 × 10 2 = 63 10 × 10 = 63 100 Therefore, 0 . 3969 = 0 . 63

Simplify: 729 + 0 . 729 3 + 0 . 0729 × 1 729

Given, 729 + 0 . 729 3 + 0 . 0729 × 1 729 Covert decimals into fractions, we get 729 + 0 . 729 3 + 0 . 0729 × 1 729 = 729 + 729 1000 3 + 729 10000 × 1 729 Using the properties of square roots and cube roots, we get = 729 + 729 3 1000 3 + 729 10000 × 1 729 = 3 × 3 × 3 × 3 × 3 × 3 + 3 × 3 × 3 × 3 × 3 × 3 3 10 × 10 × 10 3 + 3 × 3 × 3 × 3 × 3 × 3 10 × 10 × 10 × 10 × 1 3 × 3 × 3 × 3 × 3 × 3 = 3 × 3 × 3 + 3 × 3 10 + 3 × 3 × 3 10 × 10 × 1 3 × 3 × 3 = 27 + 9 10 + 27 10 × 10 × 1 27 = 2700 + 90 + 27 100 × 1 27 = 2817 100 × 1 27 = 3 × 3 × 313 100 × 1 3 × 3 × 3 = 313 300 = 1 . 043

If 2 . 25 x = x 65 . 61 , then find the value of x .

Given, 2 . 25 x = x 65 . 61 On cross-multiplying, we get x 2 = 2 . 25 × 65 . 61 = 225 100 × 6561 100 = 225 100 × 6561 100 = 3 × 3 × 5 × 5 10 × 10 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 10 × 10 = 3 × 5 10 × 3 × 3 × 3 × 3 10 = 15 10 × 81 10 If p 2 = q , then p = q Therefore, x = 15 10 × 81 10 = 9 10 15 = 0 . 9 × 3 . 87 = 3 . 48 Hence, the required answer is 3 . 48 .

E M B I B E

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>HOTS (Higher Order Thinking Skills)

Jharne De and Ranjana Kumar Solutions for Chapter: Square and Square Root; Cube and Cube Root, Exercise 4: HOTS (Higher Order Thinking Skills)

Author:Jharne De & Ranjana Kumar

Jharne De Mathematics Solutions for Exercise - Jharne De and Ranjana Kumar Solutions for Chapter: Square and Square Root; Cube and Cube Root, Exercise 4: HOTS (Higher Order Thinking Skills)

Attempt the practice questions on Chapter 3: Square and Square Root; Cube and Cube Root, Exercise 4: HOTS (Higher Order Thinking Skills) with hints and solutions to strengthen your understanding. Math Sight book solutions are prepared by Experienced Embibe Experts.

Questions from Jharne De and Ranjana Kumar Solutions for Chapter: Square and Square Root; Cube and Cube Root, Exercise 4: HOTS (Higher Order Thinking Skills) with Hints & Solutions

MEDIUM

8th CBSE

IMPORTANT

Math Sight book>Chapter 3 - Square and Square Root; Cube and Cube Root>EXERCISE 3.4>Q 7

The base and altitude of a right-angled triangle are $18 cm$ and $15 cm$ respectively. Find the measure of the hypotenuse correct up to three decimal places.