NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4.

- Squares and Square Roots Class 8 Ex 6.1
- Squares and Square Roots Class 8 Ex 6.2
- Squares and Square Roots Class 8 Ex 6.3

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 6 |

Chapter Name |
Squares and Square Roots |

Exercise |
Ex 6.4 |

Number of Questions Solved |
9 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4

**Question 1.**

Find the square root of each of the following numbers by Division method:

**Solution.**

**(i) 2304**

**(ii) 4489**

**(iii) 3481**

**(iv) 529**

**(v) 3249**

**(vi) 1369**

**(vii) 5776**

**(viii) 7921**

**(ix) 576**

**(x) 1024**

**(xi) 3136**

**(xii) 900**

**Question 2.**

Find the number of digits in the square root of each of the following numbers (without any calculation):

**(i)** 64

**(ii)** 144

**(iii)** 4489

**(iv)** 27225

**(v)** 390625.

**Solution.**

**(i) 64**

Number (n) of digits in 64 = 2 which is even.

∴ Number of digits in the square root of 64 \(\frac { n }{ 2 } =\frac { 2 }{ 2 } =1\)

**(ii) 144**

Number (n) of digits in 144 = 3 which is

∴ Number of digits in the square root of 144 \(\frac { n+1 }{ 2 } =\frac { 3+1 }{ 2 } =\frac { 4 }{ 2 } =2\)

**(iii) 4489**

Number (n) of digits in 4489 = 4 which is even.

∴ Number of digits in the square root of 4489 \(\frac { n }{ 2 } =\frac { 4 }{ 2 } =2\)

**(iv) 27225**

Number (n) of digits in 27225 = 5 which is odd.

∴ Number of digits in the square root of 27225 \(\frac { n+1 }{ 2 } =\frac { 5+1 }{ 2 } =\frac { 6 }{ 2 } =3\)

**(v) 390625**

Number (n) of digits in 390625 = 6 which is even.

∴ Number of digits in the square root of 390625 \(\frac { n }{ 2 } =\frac { 6 }{ 2 } =3\)

**Question 3.**

Find the square root of the following decimal numbers:

**(i)** 2.56

**(ii)** 7.29

**(iii)** 51.84

**(iv)** 42.25

**(v)** 31.36

**Solution.**

**(i) 2.56**

**(ii) 7.29**

**(iii) 51.84**

**(iv) 42.25**

**(v) 31.36**

**Question 4.**

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

**(i) **402

**(ii)** 1989

**(iii)** 3250

**(iv)** 825

**(v)** 4000

**Solution.**

**(i)402**

**(ii) 1989**

**(iii) 3250**

**(iv) 825**

**(v) 4000**

**Question 5.**

Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

**(i)** 525

**(ii)** 1750

**(iii)** 252

**(iv)** 1825

**(v)** 6412

**Solution.**

**(i) 525**

**(ii) 1750**

**(iii) 252**

**(iv) 1825**

**(v) 6412**

**Question 6.**

Find the length of the side of a square whose area is 441 \({ m }^{ 2 }\).

**Solution.**

Area of the square = 441 \({ m }^{ 2 }\)

∴ Length of the side of the square

**Question 7.**

In a right triangle ABC, ∠B = 90°.

**(a)** If AB = 6 cm, BC = 8 cm, find AC

**(b)** If AC 13 cm, BC = 5 cm, find AB.

**Solution.**

**(a)** In the right triangle ABC,

∠B = 90°

Given

**Question 8.**

A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

**Solution.**

Let the number of rows be x.

Then the number of columns is x.

**Question 9.**

There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

**Solution.**

Let the number of rows be x.

Then the number of columns is x.

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