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# Common Square Roots

## What are square roots and why do we care?

The square root of a number is a number that, when multiplied by itself, equals the desired value. So, for example, the square root of 49 is 7 (7x7=49). The process of multiplying a number times itself is called squaring.

Numbers whose square roots are whole numbers, (or more accurately positive integers) are called perfect square numbers. Numbers with decimals aren't perfect square roots.

All positive numbers will have a positive number as their square root, called the principal, and a negative number. These numbers are all known as real numbers.

All negative numbers will have a complex number as their square root. A complex number is a number multiplied by i. i is the "imaginary" square root of -1. It's called imaginary, but it does exist to mathematicians.

### How do we write out square roots?

A square root equation is written out using a radical sign or radical symbol (?). The number that we want to get the root of comes after or under the tail of the radical (for example ?3 if we wanted to find the square root of 3). The number after the radical is called the radicand. On a calculator, instead of the radical, you might see "sqrt".

### What do we use square roots for?

It may be a bit hard to picture it, but square roots are some of the most useful numbers around. Square root functions are super important for physics equations of all kinds. They're also valuable for statistics; statisticians use square roots all the time in analyzing the correlation between different points of data.

### List of Perfect Squares

Use this table to find the squares and square roots of numbers from 1 to 100.

You can also use this table to estimate the square roots of larger numbers.

• For instance, if you want to find the square root of 2000, look in the middle column until you find the number that is closest to 2000. The number in the middle column that is closest to 2000 is 2,025.
• Now look in at the number to the left of 2,025 to find its square root. The square root of 2,025 is 45.
• Therefore, the approximate square root of 2,000 is 45.

To get a more exact number, you will have to use a calculator (44.721 is the more exact square root of 2,000).

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 NUMBER SQUARE SQUARE ROOT 1 1 1.000 2 4 1.414 3 9 1.732 4 16 2.000 5 25 2.236 6 36 2.449 7 49 2.646 8 64 2.828 9 81 3.000 10 100 3.162 11 121 3.317 12 144 3.464 13 169 3.606 14 196 3.742 15 225 3.873 16 256 4.000 17 289 4.123 18 324 4.243 19 361 4.359 20 400 4.472 21 441 4.583 22 484 4.690 23 529 4.796 24 576 4.899 25 625 5.000 26 676 5.099 27 729 5.196 28 784 5.292 29 841 5.385 30 900 5.477 31 961 5.568 32 1,024 5.657 33 1,089 5.745 34 1,156 5.831 35 1,225 5.916 36 1,296 6.000 37 1,369 6.083 38 1,444 6.164 39 1,521 6.245 40 1,600 6.325 41 1,681 6.403 42 1,764 6.481 43 1,849 6.557 44 1,936 6.633 45 2,025 6.708 46 2,116 6.782 47 2,209 6.856 48 2,304 6.928 49 2,401 7.000 50 2,500 7.071 51 2,601 7.141 52 2,704 7.211 53 2,809 7.280 54 2,916 7.348 55 3,025 7.416 56 3,136 7.483 57 3,249 7.550 58 3,364 7.616 59 3,481 7.681 60 3,600 7.746 61 3,721 7.810 62 3,844 7.874 63 3,969 7.937 64 4,096 8.000 65 4,225 8.062 66 4,356 8.124 67 4,489 8.185 68 4,624 8.246 69 4,761 8.307 70 4,900 8.367 71 5,041 8.426 72 5,184 8.485 73 5,329 8.544 74 5,476 8.602 75 5,625 8.660 76 5,776 8.718 77 5,929 8.775 78 6,084 8.832 79 6,241 8.888 80 6,400 8.944 81 6,561 9.000 82 6,724 9.055 83 6,889 9.110 84 7,056 9.165 85 7,225 9.220 86 7,396 9.274 87 7,569 9.327 88 7,744 9.381 89 7,921 9.434 90 8,100 9.487 91 8,281 9.539 92 8,464 9.592 93 8,649 9.644 94 8,836 9.695 95 9,025 9.747 96 9,216 9.798 97 9,409 9.849 98 9,604 9.899 99 9,801 9.950 100 10,000 10.000
NOTE: Square roots in this table are rounded to the nearest thousandth.

 Mean and Median Numbers and Formulas Finding Square Roots
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