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Simplify:fraction numerator square root of 84 plus 8 over denominator 4 end fractionAnswer choices include:A. fraction numerator square root of 14 plus 4 over denominator 2 end fractionB. 2 square root of 21 plus 2C. 2 square root of 14 plus 2D. fraction numerator square root of 21 plus 4 over denominator 2 end fraction

Simplifyfraction Numerator Square Root Of 84 Plus 8 Over Denominator 4 End FractionAnswer Choices IncludeA Fraction Numerator Square Root Of 14 Plus 4 Over Deno class=

Sagot :

[tex]\frac{4+21}{2}[/tex]

1) Let's turn that from English to Math:

[tex]\frac{8+\sqrt{84}}{4}[/tex]

2) Note that we can rewrite that and then factor out the GCD to rewrite it as a product and simplify it as much as we can.

[tex]\begin{gathered} \frac{8+\sqrt{84}}{4} \\ \frac{8+\sqrt{2^2\cdot\:3\cdot\:7}}{4} \\ \frac{8+2\sqrt{21}}{4} \\ \frac{2\left(4+\sqrt{21}\right)}{4} \\ \frac{2\left(4+\sqrt{21}\right)}{2\cdot \:2} \\ \frac{4+\sqrt{21}}{2} \end{gathered}[/tex]

Note that in the options the terms are flipped, but this is not a problem. So we can tell that the answer is:

View image AubrielleD379457
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