Question

d.√1250 e. √432

Explanation:

Part d: Simplify $\boldsymbol{\sqrt{1250}}$

Step1: Factor the radicand

Factor 1250 into prime factors: $1250 = 250\times5 = 50\times5\times5 = 25\times2\times5\times5 = 25\times25\times2$. So, $1250 = 25^2\times2$.

Step2: Apply square - root property

Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a\geq0,b\geq0$) and $\sqrt{a^2}=a$ ($a\geq0$), we have $\sqrt{1250}=\sqrt{25^2\times2}=\sqrt{25^2}\times\sqrt{2}=\ 25\sqrt{2}$.

Step1: Factor the radicand

Factor 432: $432 = 144\times3=12^2\times3$.

Step2: Apply square - root property

Using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ ($a\geq0,b\geq0$) and $\sqrt{a^2}=a$ ($a\geq0$), we get $\sqrt{432}=\sqrt{12^2\times3}=\sqrt{12^2}\times\sqrt{3}=12\sqrt{3}$.

Answer:

$25\sqrt{2}$

Part e: Simplify $\boldsymbol{\sqrt{432}}$