Question

Please solve this and step wise jiska step wise nahi hua to wo answer faltu hai ........ and ha meri book ki answersheet me *Answer* 56 aaa raha hai okay ​

Answer 1

GIVEN :-

$\mapsto \sf \: \sqrt[3]{ \sqrt{46656} }$

TO FIND :-

$\mapsto \sf value \: of \: \: \sqrt[3]{ \sqrt{46656} }$

SOLUTION :-

$\mapsto \sf \: \sqrt[3]{ \sqrt{46656} }$

➫ Firstly we will find the square root of 46656.

$\Large{ \begin{array}{c|c} \tt 2& \sf{ 46656 } \\ \cline{1-2} \tt 2& \sf { 23328 } \\ \cline{1-2} \tt 2& \sf{ 11664} \\ \cline{1-2} \tt 2 & \sf{ 5832} \\ \cline{1-2} \tt 2 & \sf{2916}\\ \cline{1-2} \tt 2 & \sf{1458 }\\ \cline{1-2} \tt 3 & \sf{729} \\ \cline{1 - 2} \tt 3& \sf{243} \\ \cline{1 - 2} \tt 3& \sf{81} \\ \cline{1 - 2} \tt 3& \sf{27} \\ \cline{1 - 2} \tt 3& \sf{9} \\ \cline{1 - 2} \tt 3& \sf{3} \\ \cline{1 - 2} \tt & \sf{1}\end{array}}$

$\therefore \sf \: \sqrt{46656} = \sqrt{2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3} \\ \\ \mapsto \sf \: \sqrt{46656} = \sqrt{2 ^{2} \times 2 ^{2} \times 2^{2} \times 3 ^{2} \times 3^{2} \times 3 ^{2}} \\ \\ \mapsto \sf \: \sqrt{46656} = 2 \times 2 \times 2 \times 3 \times 3 \times 3 \\ \\ \mapsto \sf \: \sqrt{46656} = \underline{ \boxed{ \blue{ \sf 216}}}$

✒ Hence we got the value of √46656 = 216

Now,

$\mapsto \sf \: \sqrt[3]{216}$

$\Large{ \begin{array}{c|c} \tt 6& \sf{ 216 } \\ \cline{1-2} \tt 6 & \sf { 36 } \\ \cline{1-2} \tt 6& \sf{ 6} \\ \cline{1-2} \tt & \sf{ 1}\end{array}}$

$\therefore \sf \sqrt[3]{216} = \sqrt[3]{6 \times 6 \times 6} \\ \\ \mapsto \sf \: \sqrt[3]{216} = \sqrt[3]{6 ^{3} } \\ \\ \mapsto \sf \: \sqrt[3]{216} = \underline{ \boxed{ \blue{ \sf6}}}$

Now,

$\boxed{ \boxed{ \red{ \bf \sqrt[3]{ \sqrt{46656} = 6} }}}$

Hence the required answer is 6.

Answer 2

Answer :

Solution : $\sqrt[3]{\sqrt{46656} }$

First of all we have to find H.C.F of  46656  to remove square root

   

2I46656

2I23328

2I11664

2I5832

2I2916

2I1458

3I729

3I243

3I81

3I27

3I9

3I3

 I1

H.C.F = 2X2X2X2X2X2X3X3X3X3X3X3

  Hence,

$\sqrt{46656}$ = $\sqrt{2^{2}X 2^{2}X 2^{2} X3^{2}X3^{2} X 3^{2}$

            =2X2X2X3X3X3

            =216

Now, secondly we have to find H.C.F of 216 to remove cube root

3I216

3I72

3I24

2I8

2I4

2I2

 I1

H.C.F = 3X3X3X2X2X2

Hence,

$\sqrt[3]{216}$ =  $\sqrt[3]{3X3X3X2X2X2}$

        = $\sqrt[3]{3^{3} X 2^{3} }$

        = 3 X 2

        = 6

Therefore,$\sqrt[3]{\sqrt{46656} }$ = 6