NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.4 Part 7

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Using Pythagoras theorem find Squares and Square root

Using Pythagoras Theorem Find Squares and Square Root

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Question: 6 Find the length of the side of a square whose area is


Let the length of side of a square be x meter.

Area of square =

According to question,


Image of Length of the Side of a Square

Hence, the length of side of a square is 21 m.

Question: 7 In a right triangle ABC,

(i) If AB=6 cm, BC=8 cm, find AC.

(ii) IF AC= 13 cm, BC=5 cm, find AB.




Image of a Right Triangle ABC

Using Pythagoras theorem,



Using Pythagoras Theorem to Find Squares and Square Root

Using Pythagoras theorem,

Question: 8 A gardeners have 1000 plants. He wants to plant these in such a way that the number of rows and number of columns remain same. Find the minimum number of plants he needs more for this.


Here, Plants = 1000

So, here perfect square has calculated.

Hence, number should be added to make it perfect square

Hence, the gardener required 24 more plants.

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?


Here, Number of children = 500

Number of children who will left out in this arrangement has to be calculated.

So, the number which should be the square root of 500.

It shows the square of 22 is less than 500 by 16.

Hence, required perfect square is 484.

Thus, number of children who left out class is

In each row, the number of children is 22 and left out children are 16.