Question

find the product of (root 3/5 + root 5/2)and (root 5 + root 2)​

Answer 1

Answer:

Step-by-step explanation:

You can rationalize the denominator for further simplification....

Answer 2

Answer:

The product of ($\frac{\sqrt{3} }{\sqrt{5} }$ +$\frac{\sqrt{5} }{\sqrt{2} }$)  and √5+√2 = √3 +√5 +  $\frac{\sqrt{30} }{5}$  + $\frac{5\sqrt{2} }{2 }$

Step-by-step explanation:

Given two irrational numbers

($\frac{\sqrt{3} }{\sqrt{5} }$ +$\frac{\sqrt{5} }{\sqrt{2} }$)  and √5+√2

To find,

The product of the given two numbers

Recall the property

The distributive property of integers is given by

a(b+c) = a×b+ a×c

Solution:

($\frac{\sqrt{3} }{\sqrt{5} }$ +$\frac{\sqrt{5} }{\sqrt{2} }$) ×(√5+√2)

Applying distributive property we get

=  $\frac{\sqrt{3} }{\sqrt{5} }$ (√5+√2) +$\frac{\sqrt{5} }{\sqrt{2} }$×(√5+√2)

Again applying distributive property we get

=  $\frac{\sqrt{3} }{\sqrt{5} }$ ×√5+  $\frac{\sqrt{3} }{\sqrt{5} }$ ×√2) +$\frac{\sqrt{5} }{\sqrt{2} }$×√5++$\frac{\sqrt{5} }{\sqrt{2} }$×√2

= √3 + $\frac{\sqrt{6} }{\sqrt{5} }$ + $\frac{5 }{\sqrt{2} }$ + √5

= √3 +√5 +  $\frac{\sqrt{6} }{\sqrt{5} }$ ×$\frac{\sqrt{5} }{\sqrt{5} }$ + $\frac{5 }{\sqrt{2} }$ ×$\frac{\sqrt{2} }{\sqrt{2} }$

= √3 +√5 +  $\frac{\sqrt{30} }{5}$  + $\frac{5\sqrt{2} }{2 }$

∴ The product of ($\frac{\sqrt{3} }{\sqrt{5} }$ +$\frac{\sqrt{5} }{\sqrt{2} }$)  and √5+√2 = √3 +√5 +  $\frac{\sqrt{30} }{5}$  + $\frac{5\sqrt{2} }{2 }$

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