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$4 Prahsant and Katy each try to work out the answer to sqrt(3^(2)+4^(2)). Prashant writes this working. {:[sqrt(3^(2)+4^(2))],[=sqrt(3^(2))+sqrt(4^(2))],[=sqrt9+sqrt16],[=3+4],[=7]:} Katy writes this working. {:[sqrt(3^(2)+4^(2))],[=sqrt(9+16)],[=sqrt25],[=5]:} Who is correct?$

$4$ Prahsant and Katy each try to work out the answer to $\sqrt{3^{2}+4^{2}}$ . Prashant writes this working. $\newline$ $\begin{array}{l} \sqrt{3^{2}+4^{2}} \\ =\sqrt{3^{2}}+\sqrt{4^{2}} \\ =\sqrt{9}+\sqrt{16} \\ =3+4 \\ =7 \end{array}$ $\newline$ Katy writes this working. $\newline$ $\begin{array}{l} \sqrt{3^{2}+4^{2}} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{array}$ $\newline$ Who is correct?

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Math Problems

Grade 8

Identify equivalent linear expressions: word problems

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4

Prahsant and Katy each try to work out the answer to

\sqrt{3^{2}+4^{2}}

. Prashant writes this working.

\newline

\begin{array}{l} \sqrt{3^{2}+4^{2}} \\ =\sqrt{3^{2}}+\sqrt{4^{2}} \\ =\sqrt{9}+\sqrt{16} \\ =3+4 \\ =7 \end{array}

\newline

Katy writes this working.

\newline

\begin{array}{l} \sqrt{3^{2}+4^{2}} \\ =\sqrt{9+16} \\ =\sqrt{25} \\ =5 \end{array}

\newline

Who is correct?

Write Expression: Prashant's first step is to write the expression $\sqrt{3^{2}+4^{2}}$ .
Separate Square Roots: Prashant then separates the square root of the sum into the sum of two separate square roots: $\sqrt{3^{2}} + \sqrt{4^{2}}$ . This is a mistake because the square root of a sum is not equal to the sum of the square roots of the addends.