Square Root Of 3780 In Simplest Radical Form
Simplify the square root of 3780 to its lowest radical form.ANSWER: 6√105
6√105 is in the lowest radical form.
Simplified Radical Form of √3780
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 √3780, we need to divide into factors.
√3780 = √2 x √2 x √3 x √3 x √3 x √5 x √7Step 2: List Perfect Squares
1 is a perfect square and divides 3780
4 is a perfect square and divides 3780
9 is a perfect square and divides 3780
36 is a perfect square and divides 3780
Step 3: Divide To Perfect Square
Divide 3780 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 3780 in its simplest form: 6√105
How do you simplify √3780
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 3780. Divide 3780 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 6√105.
Simplified Decimal Form of √3780
The square root of 3780 is approximately 61.482 when expressed in decimal form.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√75 | 5√3 | √3 x √5 x √5 |
√92 | 2√23 | √2 x √2 x √23 |
√83 | Square root of 83 is the simplest radical form. | √83 |
√959 | Square root of 959 is the simplest radical form. | √7 x √137 |
√406 | Square root of 406 is the simplest radical form. | √2 x √7 x √29 |
√483 | Square root of 483 is the simplest radical form. | √3 x √7 x √23 |
√9951 | Square root of 9951 is the simplest radical form. | √3 x √31 x √107 |
√4723 | Square root of 4723 is the simplest radical form. | √4723 |
√8113 | Square root of 8113 is the simplest radical form. | √7 x √19 x √61 |