# CLASS-8PROBLEM & SOLUTION OF SQUARE ROOT

Problem & Solution of Powers & Roots

4

1) Find the value of followings ( 3 -------- )²

5

4                ( 3 X 5 ) + 4

Ans.) ( 3 ------- )² = [ --------------- ]²

5                      5

19²            361

= ---------- = ----------   (Ans.)

5²             25

3

2) Find the value of followings ( - 5 -------- )²

6

3                 ( 5 X 6 ) + 3

Ans.)  ( - 5 -------- )²= [ - --------------- ]²

6                       6

33²             1089

= ----------- = ------------    (Ans.)

6²                36

4

3) Find the value of followings ( - 3 -------- )

9

4                     ( 3 X 9 ) + 4

Ans.) ( - 3 -------- )  =  [ - ----------------- ]ᶟ

9                           9

31              29791

=  -  --------- = - -----------     (Ans.)

9               729

4)  Find the square root of  23.4578

Ans.)           4   ) 23.4578 ( 4.84

16

------------

88  )  745  ( 8

704

-----------

964 )  4178 ( 4

3856

-------------

322

So, the required square root is 23.4578 = 4.84  (Ans.)

9 + √6

5)  Find the value of  √ ------------

9 - √6

9 + √6

Ans.)       √ ------------

9 - √6

( 9 + √6 ) ( 9 + √6 )

=   √ ------------------------

( 9 - √6) ( 9 + √6 )

[ Multiply both numerator & denominator by 9 + √6 ]

( 9 + √6 )²

= √ -------------------

9² - (√6)²

√ ( 9 + √6 )²

=  ----------------

√ 81 – 6

( 9 + √6 )

=  ----------------

√ 75

9 + 2.45

=  --------------

8.66

11.45

=  --------------   =   1.32          (Ans.)

8.66

6) Find the square root of 11.23

Ans.) First of all, we need to add more zeros ‘0’ after given number 11.23 to get the square root up to three decimal places. So, 11.23 = 11.230000

3 ) 11.23 00 00 ( 3.351

9

-----------

63  )  223 ( 3

189

-----------

665  )  3400  ( 5

3325

-----------

6701 )  7500 ( 1

6701

-----------

799

So, the square root of 11.23 up to decimal places is 3.351 (Ans.)