Question

which equation results from isolating a radical term and squaring both sides of the equation for the equation

Answer 1

Answer:

D) c - 2 = 25 + c + 10√c

Step-by-step explanation:

The given equation is $\sqrt{c - 2} - \sqrt{c} = 5$

$\sqrt{c -2} = 5 + \sqrt{c}$

Taking square on both sides, we get

Here we used ( a+ b)^2 = a^2 + b^2 + 2ab formula.

c - 2 = 5^2 + (√c)^2 + 2(5)√c

c - 2 = 25 + c +10√c

Answer: D) c - 2 = 25 + c + 10√c

Thank you.

Answer 2

Answer:

D. $c-2=25+c+10\sqrt{c}$

Step-by-step explanation:

We have been given a radical equation $\sqrt{c-2}-\sqrt{c}=5$. We are asked to find the equation that results from isolating a radical term and squaring both sides of the equation for the equation.

Add $\sqrt{c}$ on both sides:

$\sqrt{c-2}-\sqrt{c}+\sqrt{c}=5+\sqrt{c}$

$\sqrt{c-2}=5+\sqrt{c}$

Square both sides:

$(\sqrt{c-2})^2=(5+\sqrt{c})^2$

Using radical rule $\sqrt[n]{a^n} =a$, we will get:

$c-2=(5+\sqrt{c})^2$

Using perfect square formula $(a+b)^2=a^2+2ab+b^2$, we will get:

$c-2=5^2+2*5\sqrt{c}+(\sqrt{c})^2$

$c-2=25+10\sqrt{c}+c$

$c-2=25+c+10\sqrt{c}$

Therefore, option D is the correct choice.