# SAT Math : Decimals

## Example Questions

### Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

This problem becomes much simpler if we rewrite the decimal in scientific notation

Because  has an even exponent, we can take its square root by dividing it by two. The square root of 4 is 2, and because 3.6 is a little smaller than 4, its square root is a little smaller than 2, around 1.9

### Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, and the square root of 4 is two, so the square root of 6.4 is between 3 and 2, around 2.53

### Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root.  is a perfect square, whose square root is .

### Example Question #21 : Decimals

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, so the square root of 10 should be a little larger than 3, around 3.16

### Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 36 is 6, so the square root of 40 should be a little more than 6, around 6.32.

### Example Question #1 : How To Find The Square Root Of A Decimal

Solve for :

Explanation:

Just like any other equation, isolate your variable. Start by multiplying both sides by :

Now, this is the same as:

You know that  is . You can intelligently rewrite this problem as:

, which is the same as:

### Example Question #2 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Explanation:

To find the square root of this decimal we convert it into scientific notation.

Because  has an even exponent, we can divide the exponenet by 2 to get its square root.  is a perfect square, whose square root is .

### Example Question #11 : How To Find The Square Root Of A Decimal

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 #11 : How To Find The Square Root Of A Decimal

Without using a calculator, solve for x:

Explanation:

Simplifying the given equation gives us

Therefore, the correct answer is .

### Example Question #12 : How To Find The Square Root Of A Decimal

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 .