Solved on Sep 18, 2023

Solve the equation $\sqrt{z}=23$ and find the value of $z$ .

STEP 1

Assumptions1. We are given the equation $\sqrt{z}=23$ . We need to solve for $z$

STEP 2

To solve for $z$ , we need to eliminate the square root on the left side of the equation. We can do this by squaring both sides of the equation.
$(\sqrt{z})^2 =23^2$

STEP 3

quaring the square root of $z$ gives us $z$ . Squaring23 gives us $23^2$ .
$z =23^2$

STEP 4

Calculate the value of $23^2$ .
$z =23^2 =529$ So, the solution to the equation is $z=529$ .

STEP 5

To check our solution, we substitute $z=529$ back into the original equation and see if both sides are equal.
$\sqrt{z} = \sqrt{529}$

STEP 6

Calculate the square root of529.
$\sqrt{529} =23$ Since the square root of529 is indeed23, our solution is correct.So, the solution to the equation is $z=529$ .

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Solve the equation $\sqrt{z}=23$ and find the value of $z$ .

STEP 1

Assumptions1. We are given the equation $\sqrt{z}=23$ . We need to solve for $z$

STEP 2

To solve for $z$ , we need to eliminate the square root on the left side of the equation. We can do this by squaring both sides of the equation.
$(\sqrt{z})^2 =23^2$

STEP 3

quaring the square root of $z$ gives us $z$ . Squaring23 gives us $23^2$ .
$z =23^2$

STEP 4

Calculate the value of $23^2$ .
$z =23^2 =529$ So, the solution to the equation is $z=529$ .

STEP 5

To check our solution, we substitute $z=529$ back into the original equation and see if both sides are equal.
$\sqrt{z} = \sqrt{529}$

STEP 6

Calculate the square root of529.
$\sqrt{529} =23$ Since the square root of529 is indeed23, our solution is correct.So, the solution to the equation is $z=529$ .

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Solve the equation z=23\sqrt{z}=23z​=23 and find the value of zzz.

STEP 1

Assumptions1. We are given the equation z=23\sqrt{z}=23z​=23 . We need to solve for zzz

STEP 2

To solve for zzz, we need to eliminate the square root on the left side of the equation. We can do this by squaring both sides of the equation.(z)2=232(\sqrt{z})^2 =23^2(z​)2=232

STEP 3

quaring the square root of zzz gives us zzz. Squaring23 gives us 23223^2232.z=232z =23^2z=232

STEP 4

Calculate the value of 23223^2232.z=232=529z =23^2 =529z=232=529So, the solution to the equation is z=529z=529z=529.

STEP 5

To check our solution, we substitute z=529z=529z=529 back into the original equation and see if both sides are equal.z=529\sqrt{z} = \sqrt{529}z​=529​

STEP 6

Calculate the square root of529.529=23\sqrt{529} =23529​=23Since the square root of529 is indeed23, our solution is correct.So, the solution to the equation is z=529z=529z=529.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve the equation $\sqrt{z}=23$ and find the value of $z$ .

Assumptions1. We are given the equation $\sqrt{z}=23$ . We need to solve for $z$

To solve for $z$ , we need to eliminate the square root on the left side of the equation. We can do this by squaring both sides of the equation.
$(\sqrt{z})^2 =23^2$

quaring the square root of $z$ gives us $z$ . Squaring23 gives us $23^2$ .
$z =23^2$

Calculate the value of $23^2$ .
$z =23^2 =529$ So, the solution to the equation is $z=529$ .

To check our solution, we substitute $z=529$ back into the original equation and see if both sides are equal.
$\sqrt{z} = \sqrt{529}$

Calculate the square root of529.
$\sqrt{529} =23$ Since the square root of529 is indeed23, our solution is correct.So, the solution to the equation is $z=529$ .