What should the number 3 + 5 be multiplied by to get a positive integer? Find the integer.

Given real number is 3 + 5 . The process of multiplying one rational number by another rational number to get rational number is called a rationalization. The rationalizing factor of 3 + 5 is 3 - 5 . ∴ 3 + 5 3 - 5 = 3 2 - 5 2 ∵ a + b a - b = a 2 - b 2 = 9 - 5 = 4 So, we have to multiply 3 + 5 by 3 - 5 to get an integer. Hence, 4 is the required integer.

Find the value of 3 + 5 6 + 15 .

Given expression is 3 + 5 6 + 15 . ∴ 3 + 5 6 + 15 = 3 6 + 15 + 5 6 + 15 = 18 + 45 + 30 + 75 = 9 × 2 + 9 × 5 + 30 + 25 × 3 = 3 2 + 3 5 + 30 + 5 3 Hence, the value of 3 + 5 6 + 15 is 3 2 + 3 5 + 30 + 5 3 .

Find the value of 1 7 - 1 .

We need to find the value of 1 7 - 1 . Here, we need to simplify by rationalizing the denominator. Rationalizing factor of 7 - 1 is 7 + 1 . ∴ 1 7 - 1 = 1 7 - 1 × 7 + 1 7 + 1 = 7 + 1 7 2 - 1 2 ∵ a + b a - b = a 2 - b 2 = 7 + 1 7 - 1 = 7 + 1 6 Hence, the value of 1 7 - 1 is 7 + 1 6 .

E M B I B E

MATHEMATICS CLASS 9>Arithmetic>Chapter 1 - Real Numbers>EXERCISE-1.4

Kesab Chandra Nag Solutions for Exercise 4: EXERCISE-1.4

Author:Kesab Chandra Nag

Kesab Chandra Nag Mathematics Solutions for Exercise - Kesab Chandra Nag Solutions for Exercise 4: EXERCISE-1.4

Attempt the practice questions from Exercise 4: EXERCISE-1.4 with hints and solutions to strengthen your understanding. MATHEMATICS CLASS 9 solutions are prepared by Experienced Embibe Experts.

Questions from Kesab Chandra Nag Solutions for Exercise 4: EXERCISE-1.4 with Hints & Solutions

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 1 - Real Numbers>EXERCISE-1.4>Q 2

Find the value of $\sqrt{13 + \sqrt{7 + \sqrt{4}}}$ .

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 1 - Real Numbers>EXERCISE-1.4>Q 2

What should the number $(3 + \sqrt{5})$ be multiplied by to get a positive integer? Find the integer.

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 1 - Real Numbers>EXERCISE-1.4>Q 2

What are the numbers usually denoted by $Q$ and $R$ ?

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 1 - Real Numbers>EXERCISE-1.4>Q 2

If the value of $\sqrt{18} + \sqrt{128}$ is $k \sqrt{2}$ then find the value of k.

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 1 - Real Numbers>EXERCISE-1.4>Q 2

Find the value of $(\sqrt{3} + \sqrt{5}) (\sqrt{6} + \sqrt{15})$ .

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 1 - Real Numbers>EXERCISE-1.4>Q 2

Find the value of $\frac{1}{\sqrt{7} - 1}$ .

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 1 - Real Numbers>EXERCISE-1.4>Q 2

If the quotient, when $3 \sqrt[4]{5}$ divided by $6 \sqrt[4]{4}$ is in the form of $\frac{1}{2} \sqrt[4]{\frac{m}{n}}$ , find the value of $\frac{m}{n}$ .