What is the square root of 169?

The square root of 169 is 13 – this is technically the major square source of 169.

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169 = 13

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How to discover the square root of 169

When we method the trouble like this, we room finding the square source (sqrt) of the initial number. The square source of x is a number, n, that satisfies this equation:


Every optimistic number has two square roots, a positive and also a negative.

The hopeful square source is referred to as the principal square root, and also it is generally understood to it is in the one we space interested in finding.

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In this case, we want the hopeful square source of 169.

Finding square source of 169 through factoring

To resolve 169, we can factor the number under the radical sign. Prime factorization that the very first several prime numbers will help us watch which ones can be components of the target number.

Finding determinants Of 169Prime Number (n)169 ÷ nDoes the Factor?
284.5No
356.33No
533.8No
724.14286No
1115.36No
1313Yes!
179.941No

Only one element number is a factor, 13, and it times itself gives our target number, 169.

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Rewrite the original problem, substituting our found factor because that the initial number:

169 = 13 * 13 = 132

We cannot leave the exponent under the radical. To remove exponents indigenous under radical signs, divide also exponents through 2, then move the base (in this case, 13) and also its result exponent external the radical sign.

Divide the exponent 2 through 2:

1322 = 131

Move 131 outside the radical sign and also leave 1 under the radical authorize (since 169 cannot be equal to nothing)131 = 1311


1311 is the square root of 169 in radical type – this is the most basic radical form

The brand-new result look at complicated, yet if you simplify the parts, you discover it is not:

131 = 131 = 1

This returns 13 * 1, i m sorry is 13.

The major square source of 169 is 13.

The square root of 169 is a reasonable number since it is a perfect square -- the answer has actually no decimals.

How carry out You discover The Square root Of 169 by Estimating?

Another means to discover the square root of 169 is to calculation using well-known squares.

You more than likely instantly remind 122 is 144. Is 169 an ext or less than 144? it is more, for this reason you require a bigger number.

Let"s shot 15. We calculate 152 = 225, which is as well big.

We have now learned the square root of 169 is somewhere between 12 and also 15. Shot the 2 remaining entirety numbers:

142 = 196 – obtaining closer!

132 = 169

The square source of 169 is 13.

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While -13 is additionally the square root of 169 in practice, we are constantly searching for the major square root. Uneven asked to uncover “all” the square root of 169, we store with ours answer of 13.

You have the right to verify the you have the correct square source of a number by main point the number (13) time itself (13) to see if it amounts to the target number (169):

13 * 13 = 169

Square root of 169 by division method

Long division is another way to find a square source of 169 v a calculator.

To start, job-related from ideal to left and also split the genuine number 169 right into two bag of two-digit numbers.

169 = 01- 69-

Now, you job-related on each pair separately. What is the biggest perfect square much less than or equal to 1? The prize is 1. And also the square source of 1 is also 1.

So, we placed one ~ above top and also on the bottom like this: 1 01- 69- 1  0-

Now, subtract 1 native one and bring the remaining 69 down v your answer: 1 01- 69- 1  0- 69-

The following step is to dual the number in ~ the really top, i m sorry is 1. So, 1 × 2 = 2.

Then, you usage the number 2 and also the staying number at the bottom (69) to create this math problem:

2?_ × ?_  ≤ 69

Try and also find which number fits to finish the equation. The biggest number that functions is 3. This means we have:23_ × 3_  = 69

Now, girlfriend can add 3 come the height of your long division problem and 69 in ~ the bottom; 69 minus 69 is 0, for this reason you room done. The optimal is her square root of 169.

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 1   301- 69- 1   0- 69- 0 69

The answer is 13.


What friend learned:

After working your means through this lesson and also video, you have learned:

That the square source of 169 is 13.Every hopeful number has a confident and negative square source – the positive square source is dubbed the major root.How to uncover the square root of 169 through factoring and estimatingHow to check your work