Is there a trick or formula or easy way to figure out square root mentally?
Memorize the common square roots
2 * 2 = 4
3 * 3 = 9
etc.
Then using those squares, you can estimate other square roots.
Example:
square root of 130 =
√ 121 = 11
√ 144 = 12
√ 130 is between 11 and 12
Ok. Is there an easy way to figure the perfect square root for numbers 13 through 25.
3 * 3 = 9
4 * 4 = 16
5 * 5 = 25
Memorize the squares of 1 - 12
So are u saying to memorize the squares for 13 - 25 as well? Not sure if my question is clear. For e.g. square of 23 is 529. By multiplying the last digit of 23 ( 3x3)= 9, same last digit of the number 529, is there a way I easily work out the first 2 numbers 52?
ahh, so you want to square the numbers , not take their square roots
A mental way to multiply any two 2-digit numbers
e.g.
34 x 34
4x4 = 16 , so the last digit is 6 , with 1 to carry
3x4+ 4x3 = 24 plus the one to carry is 25
so the tens digit is 5 , with 2 to carry
3x3 = 9 with 2 to carry is 11
so 34^2 = 1156
the numbers don't have to be the same ...
e.g. 56 x 83
6x3 = 18 , so unit digit is 8 , carry 1
5x3 + 6x8 = 63 , so tens digit is 4 , carry 6
5x8 = 40, plus the carry 6 = 46
56x83 = 4648
but really, am I not just doing the steps of ordinary multiplication ??
Yes, there is a relatively simple method to approximate square roots mentally. It's called the "Digit-by-Digit Method." Here's how it works:
1. Break down the number into pairs of digits, starting from the right. For example, if you want to find the square root of 6489, group it as 64 and 89.
2. Find the largest perfect square less than or equal to the first pair (64 in this case). In this case, the largest perfect square less than or equal to 64 is 64 itself.
3. Take the positive square root of the perfect square from step 2 (which is the square root of 64, equal to 8) as the first digit of the answer.
4. Move to the next pair of digits (89 in this case) and write it beside the digit you found in step 3, like 8|89.
5. Double the digit you found in step 3 (8 × 2 = 16) and insert a variable digit (let's call it x) at the end to create a new number (in this case, 16x).
6. Find the largest value of x such that 16x × x is less than or equal to 89. In this case, the largest value of x that satisfies this condition is 5 (16 × 5 × 5 = 400).
7. Append this value of x (5) to the previous digit (8) to get the next digit in the answer (85).
8. Repeat steps 5-7 by doubling the current answer digit (85 × 2 = 170) and inserting the variable digit (x) to create a new number (170x).
9. Find the largest value of x such that 170x × x is less than or equal to the remaining digits. Repeat this process until you've exhausted all pairs of digits.
10. Your final answer will be the sequence of digits you obtained in step 7 and subsequent steps. In this case, the square root of 6489 is approximately 85.
While this method provides a decent approximation, it may not always be completely accurate. For precise square roots, using a calculator or a mathematical software program is recommended.