## Maharashtra State Board Class 8 Maths Solutions Chapter 3 Indices and Cube Root Practice Set 3.2

Question 1.

Complete the following table.

S.No. |
Number |
Power of the root |
Root of the power |

1. | \((225)^{\frac{3}{2}}\) | Cube of square root of 225 | Square root of cube of 225 |

2. | \((45)^{\frac{4}{5}}\) | ||

3. | \((81)^{\frac{6}{7}}\) | ||

4. | \((100)^{\frac{4}{10}}\) | ||

5. | \((21)^{\frac{3}{7}}\) |

Solution:

S.No. |
Number |
Power of the root |
Root of the power |

1. | \((225)^{\frac{3}{2}}\) | Cube of square root of 225 | Square root of cube of 225 |

2. | \((45)^{\frac{4}{5}}\) | 4th power of 5th root of 45 | 5th root of 4th power of 45 |

3. | \((81)^{\frac{6}{7}}\) | 6th power of 7th root of 81 | 7th root of 6th power of 81 |

4. | \((100)^{\frac{4}{10}}\) | 4th power of 10th root of 100 | 10th root of 4th power of 100 |

5. | \((21)^{\frac{3}{7}}\) | Cube of 7th root of 21 | 7th root of cube of 21 |

Question 2.

Write the following numbers in the form of rational indices.

i. Square root of 5th power of 121.

ii. Cube of 4th root of 324.

iii. 5th root of square of 264.

iv. Cube of cube root of 3.

Solution:

i. \((121)^{\frac{5}{2}}\)

ii. \((324)^{\frac{3}{4}}\)

iii. \((264)^{\frac{2}{5}}\)

iv. \((3)^{\frac{3}{3}}\)