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 -------- )ᶟ
9
4 ( 3 X 9 ) + 4
Ans.) ( - 3 -------- )ᶟ = [ - ----------------- ]ᶟ
9 9
31ᶟ 29791
= - --------- = - ----------- (Ans.)
9ᶟ 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 )
[ 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.)