# SAT Math : How to find the square root of a decimal

## Example Questions

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### Example Question #381 : Arithmetic

Evaluate:

Explanation:

The square root of a number returns a positive and negative number that multiplies by itself to obtain the number inside the square root.

### Example Question #382 : Arithmetic

Without using a calculator, solve for x:

Explanation:

Simplifying the given equation gives us

Therefore, the correct answer is .

### Example Question #383 : Arithmetic

If  and , what is the value of ?

Explanation:

We are given the equation . To determine the value of , take the square root of both sides.

.

To calculate this value, take note of the following pattern:

Each succeeding radicand is  of the previous radicand, and the value of each succeeding square root is   of the previous value. Continuing the pattern:

. However, we are also given the condition that ; hence, we eliminate the extraneous solution  and conclude that the only valid solution of  is .

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