How do you simplify #-5\sqrt { 50} - \sqrt { 98}#?

2 Answers
Jim G.
Jun 17, 2018

#-32sqrt2#

Explanation:

#"using the "color(blue)"law of radicals"#

#•color(white)(x)sqrtaxxsqrtbhArrsqrt(ab)#

#"simplifying the radicals gives"#

#sqrt50=sqrt(25xx2)=sqrt25xxsqrt2=5sqrt2#

#sqrt98=sqrt(49xx2)=sqrt49xxsqrt2=7sqrt2#

#"putting the simplifications back gives"#

#(-5xx5sqrt2)-7sqrt2#

#=-25sqrt2-7sqrt2=-32sqrt2#

smendyka
Jun 17, 2018

See a solution process below:

Explanation:

First, rewrite the terms within the radicals as:

#-5sqrt(25 * 2) - sqrt(49 * 2)#

Next, use this rule for radicals to simplify the radicals:

#sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))#

#-5sqrt(25)sqrt(2) - sqrt(49)sqrt(2) =>#

#(-5 * 5sqrt(2)) - 7sqrt(2) =>#

#-25sqrt(2) - 7sqrt(2)#

Now, factor out the common term:

#(-25 - 7)sqrt(2) =>#

#-32sqrt(2)#

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