## Table of Contents

## Overview

There are 3 questions in Class 9 Maths Exercise 1.5. The questions and their solutions are explained in easy language.

## Question/Answers Class 9 Maths Exercise 1.5

S.No. | Question/Answers |

Q.1. | Find: (i) 64½ (ii) 32⅕ (iii) 125⅓ |

Ans. | (i) 64½ = (8²)½ = 8^{1} (as 2×1/2 =1) = 8(ii) 32⅕ = (2⁵)⅕ = 2 ^{1} (as 5×1/5 =1 = 2(iii) 125⅓ = (5³)⅓ = 5 ^{1 } (as 3×1/3 =1) = 5 |

Q.2. | Find: (i) 9^{3/2} (ii) 32⅖ (iii) 16¾ (iv) 125^{-1/3} |

Ans. | (i) 9^{3/2} = (3^{2})^{3/2} = 3 ^{3 } (as 2×3/2 = 3)= 27 (ii) 32 ^{2/5} = (2^{5})^{2/5} = 2 ^{2} (as 5×2/5 = 2)= 4 (iii) 16 ^{3/4 }= (2^{4})^{3/4} = 2 ^{3} (as 4×3/4 =3)= 8 (iv) 125 ^{-1/3 }= (5^{3})^{-1/3} = 5 ^{-1} (as 3x-1/3 = -1) = ⅕ |

Q.3. | Simplify: (i) 2 ^{2/3} . 2^{1/5}(ii) (1/3 ^{3})^{7}(iii) 11 ^{1/2}/11^{1/4}(iv) 7 ^{1/2} . 8^{1/2} |

Ans. | (i) 2^{2/3} . 2^{1/5} = 2^{2/3+1/5} = 2^{13/15} [as 2/3+1/5 = (10+3)/15 = 13/15 ](ii) (1/3 ^{3})^{7} = (3^{-3} )^{7 } = 3^{-21 } = 1/3^{21 } [as -3×7= -21](iii) 11 ^{1/2}/11^{1/4} = 11^{1/2 – 1/4 } = 11^{2/8 } = 11^{1/4 } [as 1/2-1/4 = (4-2)/8 = 2/8 = 1/4](iv) 7 ^{1/2} . 8^{1/2} = (7 x 8)^{1/2 }= 56^{1/2 } |

## Extra Questions

Q.1. Find the value of 2√3 + √3

Ans. 2√3 + √3 = √3 ( 2+1) = 3√3

Q.2. If x = 7+ √40, Find the value of √x + 1/√x .

Q.3. Simplify

## Other Maths Concepts

To understand maths concepts of Rational numbers, Integers, etc used in NCERT Class 9 Maths Exercise 1.5, please also check the following articles: