AP State Syllabus AP Board 8th Class Maths Solutions Chapter 6 Square Roots and Cube Roots Ex 6.4 Textbook Questions and Answers.

## AP State Syllabus 8th Class Maths Solutions 6th Lesson Square Roots and Cube Roots Exercise 6.4

Question 1.

Find the cubes of the following numbers

(1) 8

(ii) 16

(iii) 21

(iv) 30

Solution:

Number | Cube Of a Number |

i) 8 | 8^{3} = 8 × 8 × 8 = 512 |

ii) 16 | 16^{3 }= 16 × 16 × 16 = 4096 |

iii) 21 | 21^{3} = 21 × 21 × 21 = 9261 |

iv) 30 | 30^{3} = 30 × 30 × 30 = 27000 |

Question 2.

Test whether the given numbers are perfect cubes or not.

(i) 243

(ii) 516

(iii) 729

(iv) 8000

(v)2700

Solution:

Number | Cube Of a Number | Yes / No |

i) 243 | 3 × 3 × 3 × 3 × 3 = 3^{5} |
No |

ii) 516 | 2 × 2 × 3 × 43 | No |

iii) 729 | 9 × 9 × 9 = 9^{3} |
Yes |

iv) 8000 | 20 × 20 × 20 = (20)^{3} |
Yes |

v) 2700 | (30) × (30) × 3 | No |

Question 3.

Find the smallest number by which 8788 must be multiplied to obtain a perfect cube?

Solution:

The prime factorisation of 8788

= (2 × 2) × (13 × 13 × 13)

∴ From the above product 2 ¡s left in the triplet.

∴ 2 should be multiplied with 8788 we will get a perfect cube number.

Question 4.

What smallest number should 7803 be multiplied with so that the product becomes a perfect cube?

Solution:

The prime factorisation of 7803

= (3 × 3 × 3) × (17 × 17)

∴ From the above product 17 is left in

the triplet.

∴ 17 should be multiplied to 7803 then we will get a perfect cube number.

Question 5.

Find the smallest number by which 8640 must be divided so that the quotient is a perfect cube’?

Solution:

The prime factorisation of 8640

= (2 × 2 × 2) × (2 × 2 × 2) × 5 × (3 × 3 × 3)

= (2)^{3} × (2)^{3} × 5 × (3)^{3}

Question 6.

Ravi made a cuboid of plasticine ofdimensions 12cm, 8cm and 3cm. How many minimum number of such cuboids will be needed to form a cube’?

Solution:

The volume of a plasticine cuboid

= l × b × h

= 12 × 8 × 3

= 288 cm^{3}

If the minimum no. of such cuboids will be needed to form a cube then its volume be less than 288 i.e., 216 cm^{3}

∴ s^{3} = 216

s = \(\sqrt[3]{216}=\sqrt[3]{6 \times 6 \times 6}=\sqrt[3]{6^{3}}\) = 6

∴ The side of the cube 6 cm

Question 7.

Find the smallest prime number dividing the sum 3^{11} +5^{13}.

Solution:

The units digit in 3^{11} is 7

∴ The units digit in 3^{11} is 7

The units digit in 5^{13} is 5

7 + 5 = 12 is divided by a smallest prime number 2.

∴ The smallest prime number that divide the sum 311 + 513 = 2