Answer :
Sure! Let's solve each equation step-by-step and match them with the correct solution.
1. Equation 1: [tex]\(\sqrt{m} - 5 = 7\)[/tex]
- First, add 5 to both sides to isolate the square root:
[tex]\[
\sqrt{m} = 7 + 5
\][/tex]
[tex]\[
\sqrt{m} = 12
\][/tex]
- Next, square both sides to solve for [tex]\(m\)[/tex]:
[tex]\[
m = 12^2
\][/tex]
[tex]\[
m = 144
\][/tex]
- So, the solution for this equation is 144.
2. Equation 2: [tex]\(3\sqrt{y} - 18 = -3\)[/tex]
- Start by adding 18 to both sides:
[tex]\[
3\sqrt{y} = -3 + 18
\][/tex]
[tex]\[
3\sqrt{y} = 15
\][/tex]
- Next, divide both sides by 3 to get the square root by itself:
[tex]\[
\sqrt{y} = \frac{15}{3}
\][/tex]
[tex]\[
\sqrt{y} = 5
\][/tex]
- Now, square both sides to find [tex]\(y\)[/tex]:
[tex]\[
y = 5^2
\][/tex]
[tex]\[
y = 25
\][/tex]
- So, the solution for this equation is 25.
3. Equation 3: [tex]\(\sqrt{d} + 6 = 8\)[/tex]
- Subtract 6 from both sides:
[tex]\[
\sqrt{d} = 8 - 6
\][/tex]
[tex]\[
\sqrt{d} = 2
\][/tex]
- Then, square both sides to solve for [tex]\(d\)[/tex]:
[tex]\[
d = 2^2
\][/tex]
[tex]\[
d = 4
\][/tex]
- So, the solution for this equation is 4.
4. Equation 4: [tex]\(\sqrt{x} = 9\)[/tex]
- Simply square both sides to find [tex]\(x\)[/tex]:
[tex]\[
x = 9^2
\][/tex]
[tex]\[
x = 81
\][/tex]
- Thus, the solution for this equation is 81.
Let's match the solutions with each equation:
- Equation 1: Solution is 144 (Option b)
- Equation 2: Solution is 25 (Option d)
- Equation 3: Solution is 4 (Option f)
- Equation 4: Solution is 81 (Option a)
So, the correct matching is:
1. [tex]\( \sqrt{m} - 5 = 7 \)[/tex] matches with 144
2. [tex]\( 3\sqrt{y} - 18 = -3 \)[/tex] matches with 25
3. [tex]\( \sqrt{d} + 6 = 8 \)[/tex] matches with 4
4. [tex]\( \sqrt{x} = 9 \)[/tex] matches with 81
1. Equation 1: [tex]\(\sqrt{m} - 5 = 7\)[/tex]
- First, add 5 to both sides to isolate the square root:
[tex]\[
\sqrt{m} = 7 + 5
\][/tex]
[tex]\[
\sqrt{m} = 12
\][/tex]
- Next, square both sides to solve for [tex]\(m\)[/tex]:
[tex]\[
m = 12^2
\][/tex]
[tex]\[
m = 144
\][/tex]
- So, the solution for this equation is 144.
2. Equation 2: [tex]\(3\sqrt{y} - 18 = -3\)[/tex]
- Start by adding 18 to both sides:
[tex]\[
3\sqrt{y} = -3 + 18
\][/tex]
[tex]\[
3\sqrt{y} = 15
\][/tex]
- Next, divide both sides by 3 to get the square root by itself:
[tex]\[
\sqrt{y} = \frac{15}{3}
\][/tex]
[tex]\[
\sqrt{y} = 5
\][/tex]
- Now, square both sides to find [tex]\(y\)[/tex]:
[tex]\[
y = 5^2
\][/tex]
[tex]\[
y = 25
\][/tex]
- So, the solution for this equation is 25.
3. Equation 3: [tex]\(\sqrt{d} + 6 = 8\)[/tex]
- Subtract 6 from both sides:
[tex]\[
\sqrt{d} = 8 - 6
\][/tex]
[tex]\[
\sqrt{d} = 2
\][/tex]
- Then, square both sides to solve for [tex]\(d\)[/tex]:
[tex]\[
d = 2^2
\][/tex]
[tex]\[
d = 4
\][/tex]
- So, the solution for this equation is 4.
4. Equation 4: [tex]\(\sqrt{x} = 9\)[/tex]
- Simply square both sides to find [tex]\(x\)[/tex]:
[tex]\[
x = 9^2
\][/tex]
[tex]\[
x = 81
\][/tex]
- Thus, the solution for this equation is 81.
Let's match the solutions with each equation:
- Equation 1: Solution is 144 (Option b)
- Equation 2: Solution is 25 (Option d)
- Equation 3: Solution is 4 (Option f)
- Equation 4: Solution is 81 (Option a)
So, the correct matching is:
1. [tex]\( \sqrt{m} - 5 = 7 \)[/tex] matches with 144
2. [tex]\( 3\sqrt{y} - 18 = -3 \)[/tex] matches with 25
3. [tex]\( \sqrt{d} + 6 = 8 \)[/tex] matches with 4
4. [tex]\( \sqrt{x} = 9 \)[/tex] matches with 81
