Square Root Of 1648 In Simplest Radical Form

Simplify the square root of 1648 to its lowest radical form.

ANSWER: 4√103

4√103 is in the lowest radical form.

Simplified Radical Form of √1648

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 √1648, we need to divide into factors.

√1648 = √2 x √2 x √2 x √2 x √103

Step 2: List Perfect Squares

1 is a perfect square and divides 1648
4 is a perfect square and divides 1648
16 is a perfect square and divides 1648

Step 3: Divide To Perfect Square

Divide 1648 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 1648 in its simplest form: 4√103

How do you simplify √1648

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 1648. Divide 1648 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 4√103.

Simplified Decimal Form of √1648

The square root of 1648 is approximately 40.596 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√74 Square root of 74 is the simplest radical form. √2 x √37
√51 Square root of 51 is the simplest radical form. √3 x √17
√79 Square root of 79 is the simplest radical form. √79
√118 Square root of 118 is the simplest radical form. √2 x √59
√294 7√6 √2 x √3 x √7 x √7
√113 Square root of 113 is the simplest radical form. √113
√9354 Square root of 9354 is the simplest radical form. √2 x √3 x √1559
√9785 Square root of 9785 is the simplest radical form. √5 x √19 x √103
√8268 2√2067 √2 x √2 x √3 x √13 x √53

Convert any root forms to simplest radical form.

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