Square Root Of 1003 In Simplest Radical Form

Simplify the square root of 1003 to its lowest radical form.

ANSWER: Square root of 1003 is the simplest radical form.

Square root of 1003 is the simplest radical form. is in the lowest radical form.

Simplified Radical Form of √1003

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 √1003, we need to divide into factors.

√1003 = √17 x √59

Step 2: List Perfect Squares

1 is a perfect square and divides 1003

Step 3: Divide To Perfect Square

Divide 1003 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 1003 in its simplest form: Square root of 1003 is the simplest radical form.

How do you simplify √1003

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 1003. Divide 1003 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 Square root of 1003 is the simplest radical form..

Simplified Decimal Form of √1003

The square root of 1003 is approximately 31.67 when expressed in decimal form.

Calculation Table:

Square Root Answer Calculation
√28 2√7 √2 x √2 x √7
√6 Square root of 6 is the simplest radical form. √2 x √3
√48 4√3 √2 x √2 x √2 x √2 x √3
√945 3√105 √3 x √3 x √3 x √5 x √7
√385 Square root of 385 is the simplest radical form. √5 x √7 x √11
√361 19√1 √19 x √19
√2813 Square root of 2813 is the simplest radical form. √29 x √97
√8389 Square root of 8389 is the simplest radical form. √8389
√7658 Square root of 7658 is the simplest radical form. √2 x √7 x √547

Convert any root forms to simplest radical form.

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