Question

evaluate the expression $sqrt{x^{2}-y^{2}}+sqrt3{z}$ if $x = - 10$, $y = 8$, and $z = 27$.

Explanation:

Step1: Calculate $x^{2}-y^{2}$

Substitute $x = - 10$ and $y = 8$ into $x^{2}-y^{2}$.
$x^{2}-y^{2}=(-10)^{2}-8^{2}=100 - 64=36$.

Step2: Calculate $\sqrt{x^{2}-y^{2}}$

$\sqrt{x^{2}-y^{2}}=\sqrt{36}=6$.

Step3: Calculate $\sqrt[3]{z}$

Substitute $z = 27$ into $\sqrt[3]{z}$.
$\sqrt[3]{z}=\sqrt[3]{27}=3$.

Step4: Calculate the final result

Add the two - results together: $\sqrt{x^{2}-y^{2}}+\sqrt[3]{z}=6 + 3=9$.

Answer:

9