Question

Please answer fast this problem

Answer 1

The value if 3.

Step-by-step explanation:

The expression is:

$(\sqrt{32}-\sqrt{5})^{1/3}(\sqrt{32}+\sqrt{5})^{1/3}$

Simplify the expression as follows:

$(\sqrt{32}-\sqrt{5})^{1/3}(\sqrt{32}+\sqrt{5})^{1/3}=[(\sqrt{32}-\sqrt{5})(\sqrt{32}+\sqrt{5})]^{1/3}$

                                              $=[(\sqrt{32})^{2}-(\sqrt{5})^{2}]^{1/3}$

                                              $=[32-5]^{1/3}\\=27^{1/3}\\=(3^{3})^{1/3}\\=3$

Thus, the value if 3.

Answer 2

Answer:

3

Step-by-step explanation:

$( \sqrt[3]{ \sqrt{32} - \sqrt{5} } \times ( \sqrt[3]{ \sqrt{32} } + \sqrt{5} )$

This can be directly mulitplied using the property of multiplication.

→There will be no change in the sign, Neither will affect the equations !!

Now,Multiplying internally,

$\sqrt[3]{( \sqrt{32} - \sqrt{5}) \times ( \sqrt{32} + \sqrt{5} )}$

Now,

Multiplying internally,

According to formula,

(a+b)(a-b)=a²-b²

Here,

$= > \sqrt[3]{ { \sqrt{(32)} }^{2} - \sqrt{( {5}^{2} )} }$

$= > \sqrt[3]{32 - 5} roots \: cancelled$

$= > \sqrt[3]{27}$

$\sqrt[3]{3 \times 3 \times 3}$

=>(3)³^1/3

=> 3

so,the value of above expression is 3 .

Ans.