900
Answers
Answer:
Square root of 900 = 30
Step-by-step explanation:
Answer is 30
Here we will define, analyze, simplify, and calculate the square root of 900. We start off with the definition and then answer some common questions about the square root of 900. Then, we will show you different ways of calculating the square root of 900 with and without a computer or calculator. We have a lot of information to share, so let's get started!
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Square root of 900 definition
The square root of 900 in mathematical form is written with the radical sign like this √900. We call this the square root of 900 in radical form. The square root of 900 is a quantity (q) that when multiplied by itself will equal 900.
√900 = q × q = q2
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Is 900 a perfect square?
900 is a perfect square if the square root of 900 equals a whole number. As we have calculated further down on this page, the square root of 900 is a whole number.
900 is a perfect square.
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Is the square root of 900 rational or irrational?
The square root of 900 is a rational number if 900 is a perfect square. It is an irrational number if it is not a perfect square. Since 900 is a perfect square, it is rational number. This means that the answer to "the square root of 900?" will have no decimals.
√900 is a rational number
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Can the square root of 900 be simplified?
A square root of a perfect square can be simplified because the square root of a perfect square will equal a whole number:
√900 = 30
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How to calculate the square root of 900 with a calculator
The easiest and most boring way to calculate the square root of 900 is to use your calculator! Simply type in 900 followed by √x to get the answer. We did that with our calculator and got the following answer:
√900 = 30
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How to calculate the square root of 900 with a computer
If you are using a computer that has Excel or Numbers, then you can enter SQRT(900) in a cell to get the square root of 900. Below is the result we got:
SQRT(900) = 30
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What is the square root of 900 written with an exponent?
All square roots can be converted to a number (base) with a fractional exponent. The square root of 900 is no exception. Here is the rule and the answer to "the square root of 900 converted to a base with an exponent?":
√b = b½
√900 = 900½
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How to find the square root of 900 by long division method
Here we will show you how to calculate the square root of 900 using the long division method. This is the lost art of how they calculated the square root of 900 by hand before modern technology was invented.
Step 1)
Set up 900 in pairs of two digits from right to left:
0900
Step 2)
Starting with the first set: the largest perfect square less than or equal to 9 is 9, and the square root of 9 is 3. Therefore, put 3 on top and 9 at the bottom like this:
309009
Step 3)
Calculate 9 minus 9 and put the difference below. Then move down the next set of numbers.
309009000
Step 4)
Double the number in green on top: 3 × 2 = 6. Then, use 6 and the bottom number to make this problem:
6? × ? ≤ 0
The question marks are "blank" and the same "blank". With trial and error, we found the largest number "blank" can be is 0. Replace the question marks in the problem with 0 to get:
60 × 0 = 0.
Now, enter 0 on top, and 0 at the bottom:
3009009000000
The difference between the bottom two numbers is zero, therefore, you are done! The answer is the green numbers on top. Once again, the square root of 900 is 30.