# What is the square root of 784?

Sep 16, 2015

$28$

#### Explanation:

-Write down the factors of $784$ and and see if they share the same with the choices.
- For example, if you see $27$ and $29$, you can tell that there is no factor of $27$ or $29$ in 576 since they are prime number and eliminate them.
- At this time you verify one by multiplying $28 \times 28$ to verify.

Recheck:

$28 \times 28 = 784$

Apr 12, 2017

The square root of $784 = 28$

#### Explanation:

It is beneficial to be able to estimate, or calculate exactly the square root of any number when a calculator is not present.

For this example, we can start an estimation limit high and low as follows:

$20 \times 20 = 400$ is too low

$30 \times 30 = 900$ is too high, but closer to $784$

If we raise the lower limit to $25$:

$25 \times 25 = 625$ is still too low, but closer.

Now our range is $26 \to 29$.

But the squared number ends in $4$, and the only number in our range multiplied by itself to result in a $4$ would be $8 \times 8$.

So the Square root of $784 = 28$

Apr 12, 2017

$28$

#### Explanation:

The square root of $784 = 28$.
Kindly use a calculator for these questions,.

$\sqrt{784} = 28$

If want to recheck the answer, multiply

$28 \times 28 = 784$

Apr 12, 2017

If you still have doubts use a prime factor tree.

$\sqrt{784} = 28$

#### Explanation:

You are looking for squared values that are factors of 784. Use the lowest value prime numbers that you can. Good idea to commit some of them to memory. It will pay off in the end. You can find lists of them all over the internet.

From the factor tree we have:

$\sqrt{{2}^{2} \times {2}^{2} \times {7}^{2}} = 2 \times 2 \times 7 = 28$