Square Root Of 1600 In Simplest Radical Form
Simplify the square root of 1600 to its lowest radical form.ANSWER: 40√1
40√1 is in the lowest radical form.
Simplified Radical Form of √1600
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 √1600, we need to divide into factors.
√1600 = √2 x √2 x √2 x √2 x √2 x √2 x √5 x √5Step 2: List Perfect Squares
1 is a perfect square and divides 1600
4 is a perfect square and divides 1600
16 is a perfect square and divides 1600
25 is a perfect square and divides 1600
64 is a perfect square and divides 1600
100 is a perfect square and divides 1600
400 is a perfect square and divides 1600
1600 is a perfect square and divides 1600
Step 3: Divide To Perfect Square
Divide 1600 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 1600 in its simplest form: 40√1
How do you simplify √1600
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 1600. Divide 1600 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 40√1.
Simplified Decimal Form of √1600
The square root of 1600 is approximately 40 when expressed in decimal form and you can find additive inverse of a decimal number.
Calculation Table:
| Square Root | Answer | Calculation |
|---|---|---|
| √60 | 2√15 | √2 x √2 x √3 x √5 |
| √68 | 2√17 | √2 x √2 x √17 |
| √32 | 4√2 | √2 x √2 x √2 x √2 x √2 |
| √637 | 7√13 | √7 x √7 x √13 |
| √321 | Square root of 321 is the simplest radical form. | √3 x √107 |
| √595 | Square root of 595 is the simplest radical form. | √5 x √7 x √17 |
| √4251 | Square root of 4251 is the simplest radical form. | √3 x √13 x √109 |
| √6571 | Square root of 6571 is the simplest radical form. | √6571 |
| √1580 | 2√395 | √2 x √2 x √5 x √79 |