Question

rationalize the denominator
7/5-3 root 2​

Answer 1

Answer:

5+3√2

Step-by-step explanation:

7/5-3√2

=>7×5+3√2/5-3√2×5+3√2

=>7(5+3√2)÷(5)×(5)-(3√2)×(3√2)

=>7(5+3√2)÷25-18

=>7(5+3√2)÷7

=>(5+3√2) ans

Answer 2

$\displaystyle \sf \frac{7}{5 - 3 \sqrt{2} } =\bf 5 + 3 \sqrt{2}$

Given :

$\displaystyle \sf \frac{7}{5 - 3 \sqrt{2} }$

To find :

To rationalize the denominator

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf \frac{7}{5 - 3 \sqrt{2} }$

Step 2 of 2 :

Rationalize the denominator

$\displaystyle \sf \frac{7}{5 - 3 \sqrt{2} }$

Multiplying both of the numerator and denominator by 5 + 3√2 we get

$\displaystyle \sf = \frac{7(5 + 3 \sqrt{2}) }{(5 - 3 \sqrt{2})(5 + 3 \sqrt{2} ) }$

$\displaystyle \sf = \frac{7(5 + 3 \sqrt{2}) }{ {(5)}^{2} - {(3 \sqrt{2}) }^{2} }$

$\displaystyle \sf = \frac{7(5 + 3 \sqrt{2}) }{25 - 18 }$

$\displaystyle \sf = \frac{7(5 + 3 \sqrt{2}) }{7 }$

$\displaystyle \sf = 5 + 3 \sqrt{2}$

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