Square Root Of 18974736 In Simplest Radical Form
Simplify the square root of 18974736 to its lowest radical form.ANSWER: 4356√1
4356√1 is in the lowest radical form.
Simplified Radical Form of √18974736
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 √18974736, we need to divide into factors.
√18974736 = √2 x √2 x √2 x √2 x √3 x √3 x √3 x √3 x √11 x √11 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 18974736
4 is a perfect square and divides 18974736
9 is a perfect square and divides 18974736
16 is a perfect square and divides 18974736
36 is a perfect square and divides 18974736
81 is a perfect square and divides 18974736
121 is a perfect square and divides 18974736
144 is a perfect square and divides 18974736
324 is a perfect square and divides 18974736
484 is a perfect square and divides 18974736
1089 is a perfect square and divides 18974736
1296 is a perfect square and divides 18974736
1936 is a perfect square and divides 18974736
4356 is a perfect square and divides 18974736
9801 is a perfect square and divides 18974736
14641 is a perfect square and divides 18974736
17424 is a perfect square and divides 18974736
39204 is a perfect square and divides 18974736
58564 is a perfect square and divides 18974736
131769 is a perfect square and divides 18974736
156816 is a perfect square and divides 18974736
234256 is a perfect square and divides 18974736
527076 is a perfect square and divides 18974736
1185921 is a perfect square and divides 18974736
2108304 is a perfect square and divides 18974736
4743684 is a perfect square and divides 18974736
18974736 is a perfect square and divides 18974736
Step 3: Divide To Perfect Square
Divide 18974736 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 18974736 in its simplest form: 4356√1
How do you simplify √18974736
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 18974736. Divide 18974736 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 4356√1.
Simplified Decimal Form of √18974736
The square root of 18974736 is approximately 4356 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √37 | Square root of 37 is the simplest radical form. | √37 |
| √23 | Square root of 23 is the simplest radical form. | √23 |
| √45 | 3√5 | √3 x √3 x √5 |
| √421 | Square root of 421 is the simplest radical form. | √421 |
| √243 | 9√3 | √3 x √3 x √3 x √3 x √3 |
| √962 | Square root of 962 is the simplest radical form. | √2 x √13 x √37 |
| √4433 | Square root of 4433 is the simplest radical form. | √11 x √13 x √31 |
| √3358 | Square root of 3358 is the simplest radical form. | √2 x √23 x √73 |
| √2654 | Square root of 2654 is the simplest radical form. | √2 x √1327 |