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Ncert Solutions for Square roots Class 8 CBSE Part 2



In this page we have NCERT book Solutions for Class 8th Maths:Square roots for EXERCISE 2 . Hope you like them and do not forget to like , social share and comment at the end of the page.

Question 1

 Find the square of the following numbers.

(i) 32

 (ii) 35

 (iii) 86

 (iv) 93

 (v) 71

 (vi) 46

 

Answer

1) 322

We can find the square using direct multiplication

= 32 x 32 = 1024

But above method can be cumbersome to calculate. We  can calculate such values in the another better way f

Since, 32 can be written as (30+2)

So, 322 = (30+2)2 = (30+2)(30+2)

Now we know the identity

(a+b)2= a2 + b2 +2ab

 = 302 + 2 x 30 x 2 + 22

= 900 + 120  + 4 = 1024

2) (35)2 = (30+5)2

Solving on similar lines as above

= 302 + 2 x 30 x 5  + 52

= 900 + 300 + 25 = 1225

3) 862 = (80 + 6)2

= 802 + 2 x  80 x 6  + 62

= 6400 + 960 + 36 = 7396

 

4) 932 = (90+3)2

= 90 2 +2 x 90 x 3  + 3 2

= 8100 + 540 + 9 = 8649

 

5) 71 2 = (70 + 1) 2

= 702 +2 x 70 x 1  + 1 x 1

= 4900 + 140 + 1 = 5040 + 1 = 5041

 

6) 462 = (40+6)2

= 40 2 + 2 x 40 x 6  + 62

= 1600 + 480 + 36 = 2080 + 36 = 2116

 

 

Question: 2

 Write a Pythagorean triplet whose one member is:

(i) 6

 (ii) 14

 (iii) 16

 (iv) 18

Answer

As we know 2n, n 2 + 1 and n2 - 1 form a Pythagorean triplet for any number, n > 1.

1) If we take n 2 + 1 or  n2 - 1 to be 6 then then the value of n will  not integer(n2  will be 5 or 7)

So  we can  2n = 6

Therefore, n = 3

And, n2 + 1 = 3 2 + 1= 9 + 1 = 10

And,n 2 - 1 = 3 2 - 1 = 9 - 1 = 8

Test: 6 2 + 8 2 = 36 + 64 = 100 = 102

Hence, the triplet is 6, 8, and 10 Answer

2) If we take n 2 + 1 or  n2 - 1 to be 14 then then the value of n will  not integer(n2  will be 15 or 13)

So we can take 2n= 14, therefore, n = 7

Now, n 2 + 1 = 7 2 + 1 = 49 + 1 = 50

And, n2 - 1 = 7 2 - 1 = 49 - 1 = 48

Test: 14 2 + 48 2 = 196 + 1304 = 2500 = 50 2

Hence, the triplet is 14, 48, and 50 Answer

3) If we take n 2 + 1 or  n2 - 1 to be 16 then then the value of n will  not integer(n2  will be 17 or 15)

Let us assume 2n = 16, then n = 8

Now, n2 + 1 = 8 2 + 1 = 64 + 1 = 65

And, n 2 - 1 = 8 2 - 1 = 64 - 1 = 63

Test: 162 + 63 2 = 256 + 3969 = 4225 = 65 2

Hence, the triplet is 16, 63, and 65 Answer

4) If we take n 2 + 1 or  n2 - 1 to be 18 then then the value of n will  not integer(n2  will be 19 or 17)

Let us assume 2n = 18, therefore, n = 9

Now, n 2 + 1 = 9 2 + 1 = 81 + 1 = 82

And, n 2 - 1 = 9 2 - 1 = 81 - 1 = 80

Test: 18 2 + 80 2 = 324 + 6400 = 6724 = 82 2

 


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