Question

solve. check your solutions

1. $sqrt{x}=10$
2. $5=sqrt{x-2}-1$
3. $sqrt{x+3}=5$

Explanation:

Step1: Solve $\sqrt{x}=10$

Square both sides:
$$(\sqrt{x})^2 = 10^2$$
$$x = 100$$
Check: $\sqrt{100}=10$, which matches the original equation.

Step2: Solve $5=\sqrt{x-2}-1$

Isolate the square root:
$$\sqrt{x-2}=5+1$$
$$\sqrt{x-2}=6$$
Square both sides:
$$(\sqrt{x-2})^2 = 6^2$$
$$x-2=36$$
$$x=36+2=38$$
Check: $\sqrt{38-2}-1=\sqrt{36}-1=6-1=5$, which matches the original equation.

Step3: Solve $\sqrt{x+3}=5$

Square both sides:
$$(\sqrt{x+3})^2 = 5^2$$
$$x+3=25$$
$$x=25-3=22$$
Check: $\sqrt{22+3}=\sqrt{25}=5$, which matches the original equation.

Answer:

1. $x=100$
2. $x=38$
3. $x=22$