Square Root Of 1815 In Simplest Radical Form
Simplify the square root of 1815 to its lowest radical form.ANSWER: 11√15
11√15 is in the lowest radical form.
Simplified Radical Form of √1815
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 √1815, we need to divide into factors.
√1815 = √3 x √5 x √11 x √11Step 2: List Perfect Squares
1 is a perfect square and divides 1815
121 is a perfect square and divides 1815
Step 3: Divide To Perfect Square
Divide 1815 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 1815 in its simplest form: 11√15
How do you simplify √1815
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 1815. Divide 1815 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 11√15.
Simplified Decimal Form of √1815
The square root of 1815 is approximately 42.603 when expressed in decimal form.
Calculation Table:
Square Root | Answer | Calculation |
---|---|---|
√42 | Square root of 42 is the simplest radical form. | √2 x √3 x √7 |
√23 | Square root of 23 is the simplest radical form. | √23 |
√10 | Square root of 10 is the simplest radical form. | √2 x √5 |
√458 | Square root of 458 is the simplest radical form. | √2 x √229 |
√315 | 3√35 | √3 x √3 x √5 x √7 |
√523 | Square root of 523 is the simplest radical form. | √523 |
√3343 | Square root of 3343 is the simplest radical form. | √3343 |
√3277 | Square root of 3277 is the simplest radical form. | √29 x √113 |
√3749 | Square root of 3749 is the simplest radical form. | √23 x √163 |