Square Root Of 8100 In Simplest Radical Form
Simplify the square root of 8100 to its lowest radical form.ANSWER: 90√1
90√1 is in the lowest radical form.
Simplified Radical Form of √8100
One of the main facts used to simplify square roots is that the square root of a product is equal to the product of square roots: √(x×y) = √x×√y
Explanation:
When we find square root of any number, we take one number from each pair of the same numbers from its prime factorization and we multiply them.
Step 1: List Factors
To simplify √8100, we need to divide into factors.
√8100 = √2 x √2 x √3 x √3 x √3 x √3 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 8100
4 is a perfect square and divides 8100
9 is a perfect square and divides 8100
25 is a perfect square and divides 8100
36 is a perfect square and divides 8100
81 is a perfect square and divides 8100
100 is a perfect square and divides 8100
225 is a perfect square and divides 8100
324 is a perfect square and divides 8100
900 is a perfect square and divides 8100
2025 is a perfect square and divides 8100
8100 is a perfect square and divides 8100
Step 3: Divide To Perfect Square
Divide 8100 by the largest perfect square you found in the previous step:
Step 4: Calculate The Square Root
Calculate the square root of the largest perfect square:
Final Step :
Put Steps 3 and 4 together to get the square root of 8100 in its simplest form: 90√1
How do you simplify √8100
The general approach is to first check if it is a perfect square. If so, you have the answer. If it is not a perfect square, see if any of its factors are perfect squares, or can be combined to make square numbers.
Find the lowest prime number that can divide 8100. Divide 8100 repeatedly using the long division method till you reach 1.
A pair of factor 'twins' under a square root sign (radical) form a single factor outside of it.
Factors that do not have a twin remain under the radical. Multiply them back together and leave them in there.
So, the answer is 90√1.
Simplified Decimal Form of √8100
The square root of 8100 is approximately 90 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √39 | Square root of 39 is the simplest radical form. | √3 x √13 |
| √74 | Square root of 74 is the simplest radical form. | √2 x √37 |
| √74 | Square root of 74 is the simplest radical form. | √2 x √37 |
| √500 | 10√5 | √2 x √2 x √5 x √5 x √5 |
| √634 | Square root of 634 is the simplest radical form. | √2 x √317 |
| √852 | 2√213 | √2 x √2 x √3 x √71 |
| √3422 | Square root of 3422 is the simplest radical form. | √2 x √29 x √59 |
| √4173 | Square root of 4173 is the simplest radical form. | √3 x √13 x √107 |
| √9103 | Square root of 9103 is the simplest radical form. | √9103 |