Square Root Calculator. Find The Square Root In One Easy Step

Maybe we aren't being very modest, but we think that the best answer to the question of how to find the square root is straightforward: use the square root calculator! You can use it both on your computer and your smartphone to quickly estimate the square root of a given number. Unfortunately, there are sometimes situations when you can only rely on yourself. What then? To prepare for this, you should remember several basic perfect square roots:

• Square root of 1: √1 = 1, since 1 × 1 = 1;

• Square root of 4: √4 = 2, since 2 × 2 = 4;

• Square root of 9: √9 = 3, since 3 × 3 = 9;

• Square root of 16: √16 = 4, since 4 × 4 = 16;

• Square root of 25: √25 = 5, since 5 × 5 = 25;

• Square root of 36: √36 = 6, since 6 × 6 = 36;

• Square root of 49: √49 = 7, since 7 × 7 = 49;

• Square root of 64: √64 = 8, since 8 × 8 = 64;

• Square root of 81: √81 = 9, since 9 × 9 = 81;

• Square root of 100: √100 = 10, since 10 × 10 = 100;

• Square root of 121: √121 = 11, since 11 × 11 = 121; and

• Square root of 144: √144 = 12, since 12 × 12 = 144.

The above numbers are the simplest square roots because every time you obtain an integer. Try to remember them! But what can you do when a number doesn't have such a nice square root? There are multiple solutions. First of all, you can try to predict the result by trial and error. Let's say that you want to estimate the square root of 52:

1. You know that √49 = 7 and √64 = 8, so √52 should be between 7 and 8.

2. Number 52 is closer to the 49 (effectively closer to the 7), so you can try guessing that √52 is 7.3.

3. Then, you square 7.3, obtaining 7.3² = 53.29 (as the square root formula says), which is higher than 52. You have to try with a smaller number, let's say 7.2.

4. The square of 7.2 is 51.84. Now you have a smaller number, but much closer to the 52. If that accuracy satisfies you, you can end estimations here. Otherwise, you can repeat the procedure with a number chosen between 7.2 and 7.3,e.g., 7.22, and so on and so forth.

Another approach is to simplify the square root first and then use approximations for square roots of the prime numbers (typically rounded to two decimal places):

• Square root of 2: √2 ≈ 1.41;
• Square root of 3: √3 ≈ 1.73;
• Square root of 5: √5 ≈ 2.24;
• Square root of 7: √7 ≈ 2.65;
• Square root of 11: √11 ≈ 3.32;
• Square root of 13: √13 ≈ 3.61;
• Square root of 17: √17 ≈ 4.12;
• Square root of 19: √19 ≈ 4.34; etc.

Let's try and find the square root of 52 again. You can simplify it to √52 = 2√13 (you will learn how to simplify square roots in the next section) and then substitute √13 ≈ 3.61. Finally, make a multiplication √52 ≈ 2 × 3.61 = 7.22. The result is the same as before!