Question

simplify please massage me if any one know​

Answer 1

Step-by-step explanation:

$\huge \mathrm{ \underline{Question:}}$

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} }$

$\huge \mathrm{ \underline{Solution:}}$

• In question here is three terms. So we have to rationalise each term one by one and then after rationalising the denominator, we arrange that all rationalised values according to the given question and simplify that and then after simplifying that and last we get the final answer.

Let's solve the que...on!

Rationalising each term, we get

$\mathrm{First \: term} : \frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} }$

$= \frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \frac{ \sqrt{10} - \sqrt{3} }{ \sqrt{10} - \sqrt{3} }$

$= \frac{7 \sqrt{3} ( \sqrt{10} - \sqrt{3}) }{( \sqrt{10} + \sqrt{3} )( \sqrt{10} - \sqrt{3} )}$

$= \frac{7 \sqrt{3}( \sqrt{10} - \sqrt{3} ) }{( \sqrt{10} ) - ( \sqrt{3} )} \: \: \: [∴(a + b)(a - b) = {a}^{2} - {b}^{2} ]$

$= \frac{7 \sqrt{3}( \sqrt{10} - \sqrt{3} ) }{10 - 3}$

$= \frac{ \cancel{7 }\sqrt{3}( \sqrt{10} - \sqrt{3} )}{ \cancel{7}}$

$= \red{7( \sqrt{10} - \sqrt{3} )}$

$\mathrm{Second \: term:} \: \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} }$

$= \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{6} }$

$= \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5} ) }{( \sqrt{6} + \sqrt{5})( \sqrt{6} - \sqrt{5} ) }$

$= \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5} )}{( \sqrt{6}) - ( \sqrt{5} ) } \: \: \: [∴(a + b)(a - b) = {a}^{2} - {b}^{2} ]$

$= \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5} ) }{6 - 5}$

$= \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5}) }{1}$

$= \red{2 \sqrt{5} ( \sqrt{6} - \sqrt{5}) }$

$\mathrm{Third \: term : } \: \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} }$

$= \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } \times \frac{ \sqrt{15} - 3 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} }$

$= \frac{3 \sqrt{2} ( \sqrt{15} - 3 \sqrt{2}) }{ \sqrt{15} + 3 \sqrt{2} )( \sqrt{15} - 3 \sqrt{2} ) }$

$= \frac{3 \sqrt{2} ( \sqrt{15} - 3 \sqrt{2}) }{( \sqrt{15} {)}^{2} - (3 \sqrt{2} {)}^{2} } \: \: \:[∴(a + b)(a - b) = {a}^{2} - {b}^{2} ]$

$= \frac{3 \sqrt{2}( \sqrt{15} - 3 \sqrt{2} ) }{15 - 18}$

$= \frac{ \cancel{3 }\sqrt{2} ( \sqrt{15} - 3 \sqrt{2}) }{ \cancel{3}}$

$= \red{3 \sqrt{2} ( \sqrt{15} - 3 \sqrt{2} )}$

Now arranging all the rationalised values according to the given question and simplify:

$∴ \: \sqrt{3} ( \sqrt{10} - \sqrt{3}) - 2 \sqrt{5} ( \sqrt{6} - \sqrt{5} ) + \sqrt{2}( \sqrt{15} - 3 \sqrt{2})$

$⟹ {\sqrt{30} } - 3 - 2 \sqrt{30} + 10 + \sqrt{30} - 6$

$⟹ \cancel{2 \sqrt{30} } - 9 - \cancel{2 \sqrt{30} } + 10$

$⟹ - 9 + 10$

$⟹1 \: ans.$

Used Key knowledge:-

• If the denominator is of the form √a+√b , then we multiply the numerator and denomination by √a-√b to rationalise the denominator.

Similarly

• If the denominator is of the form √a-√b , then we multiply the numerator and denomination by √a+√b to rationalise the denominator

Used formulae:—

• (a+b)(a-b) = a² - b²
• (a-b)(a+b) = a² - b²

Learn more:

# Brainly

how many terms are there in an expression

12ab -24b +36a

https://brainly.in/question/22764723