Question

find rationalization factors and find products
a)root7
b)3root5
c)-3root 8
d)root8-5
e)root10-root3

please answer it fast ​

Answer 1

$i ) Rationalising \: Factors \:of \: \sqrt{7} \: is \sqrt{7}$

$\green { Product} \\= \sqrt{7} \times \sqrt{7} \\= 7 \: \blue { ( Rational \: number )}$

$ii ) Rationalising \: Factors \:of \: 3\sqrt{5} \: is \sqrt{5}$

$\green { Product} \\= 3\sqrt{5} \times \sqrt{5} \\= 3 \times 5 \\= 15 \: \blue { ( Rational \: number )}$

$iii ) -3 \sqrt{8} \\= -3 \times 2\sqrt{2}\\= -6\sqrt{2}$

$Rationalising \: Factors \:of \: -6\sqrt{2} \: is \sqrt{2}$

$\green { Product} \\= -6\sqrt{2} \times \sqrt{2} \\= -6 \times 2 \\= -12 \: \blue { ( Rational \: number )}$

$iv ) \sqrt{8} - 5 \\= 2\sqrt{2} - 5$

$Rationalising \: Factors \:of \: 2(\sqrt{2} -5 )\: is (\sqrt{2} +5)$

$\green { Product} \\= 2(\sqrt{2}-5) \times (\sqrt{2}+5) \\= 2[\sqrt{2}^{2} - 5^{2}] \\= 2(2-25)\\= 2(-23) \\= -43 \: \blue { ( Rational \: number )}$

$v) Rationalising \: Factors \:of \: (\sqrt{10} -\sqrt{3} )\: is (\sqrt{10} +\sqrt{3})$

$\green { Product} \\= (\sqrt{10}-\sqrt{3}) \times (\sqrt{10}+\sqrt{3}) \\= [\sqrt{10}^{2} - \sqrt{3}^{2}] \\= 10 - 3\\= 7\: \blue { ( Rational \: number )}$

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