Question

Simplify: 4√20 + 3√45 − 5√5

Answer 1

$\large\bold\red{Question}$

Simplify: 4√20 + 3√45 − 5√5

$\large\bold\blue{\underline{\underline{Solution}}}$

$\sf{Step\:1:}$ Simplify the radical expressions

Factor out the perfect square

$\implies \sf4 \sqrt{2 {}^{2} \times 5}$

$\bold\red{Note:}$ The root of a product is equal to the product of the roots of each factor

$\implies \sf4 \sqrt{2 {}^{2} \sqrt{5} }$

Reduce the index of the radical and exponent with 2

$\implies \sf4 \times 2 \sqrt{5}$

Calculate the product

$\implies \sf 8 \sqrt{5}$

• Simplify again the radical expressions

Factor out the perfect square

$\implies \sf \: 3 \sqrt{3 {}^{2} \times 5}$

$\bold\red{Note:}$ The root of a product

is equal to the product of the roots of each factor

$\implies \sf \: 3 \sqrt{3 {}^{2} \sqrt{5}}$

Reduce the index of the radical and exponent with 2

$\implies \sf \: 3 \times 3 \sqrt{5}$

Calculate the product

$\implies \sf \: 9 \sqrt{5}$

$\sf{Lastly:}$ Collect like terms by calculating the sum or difference of their coefficients

$\sf8 \sqrt{5} + 9 \sqrt{5} - 5 \sqrt{5}$

$\implies \sf(8 + 9 - 5) \sqrt{5}$

Calculate the sum or difference

$\implies \sf12 \sqrt{5}$

$\sf \: thus, \: the \: answer \: is \: \sf\green{\boxed{12 \sqrt{5}}}$

hope this help!