Square Root Of 4900 In Simplest Radical Form
Simplify the square root of 4900 to its lowest radical form.ANSWER: 70√1
70√1 is in the lowest radical form.
Simplified Radical Form of √4900
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 √4900, we need to divide into factors.
√4900 = √2 x √2 x √5 x √5 x √7 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 4900
4 is a perfect square and divides 4900
25 is a perfect square and divides 4900
49 is a perfect square and divides 4900
100 is a perfect square and divides 4900
196 is a perfect square and divides 4900
1225 is a perfect square and divides 4900
4900 is a perfect square and divides 4900
Step 3: Divide To Perfect Square
Divide 4900 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 4900 in its simplest form: 70√1
How do you simplify √4900
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 4900. Divide 4900 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 70√1.
Simplified Decimal Form of √4900
The square root of 4900 is approximately 70 when expressed in decimal form.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √5 | Square root of 5 is the simplest radical form. | √5 |
| √20 | 2√5 | √2 x √2 x √5 |
| √72 | 6√2 | √2 x √2 x √2 x √3 x √3 |
| √501 | Square root of 501 is the simplest radical form. | √3 x √167 |
| √656 | 4√41 | √2 x √2 x √2 x √2 x √41 |
| √546 | Square root of 546 is the simplest radical form. | √2 x √3 x √7 x √13 |
| √8499 | Square root of 8499 is the simplest radical form. | √3 x √2833 |
| √7014 | Square root of 7014 is the simplest radical form. | √2 x √3 x √7 x √167 |
| √4579 | Square root of 4579 is the simplest radical form. | √19 x √241 |