Square Root of 1681

The square root of 1681 is a number that when multiplied by itself twice produces the original number 1681. Since it can be expressed in the form p/q, the square root of 1681 is a rational number. In this lesson, we will learn how to calculate the square root of 1681 using two methods: long division and prime factorization, both with detailed explanations.

Table of Contents:

• What is the Value of the Square Root of 1681?
• Radical Form of Square Root of 1681
• Prime Factorization Method to Find √1681
• Long Division Method to Find √1681
• Examples
• FAQs

What is the Value of the Square Root of 1681?

When a number is multiplied by itself and the result is 1681, the number is said to be the square root of 1681. The square root of 1681 is symbolically rendered as √1681.

So, √1681 = √(Number × Number)

As a result, multiplying the number 41 two times, we get the original number 1681.

(i.e) √1681 = √(41× 41)

√1681 = √(41)²

After eliminating square and square root, we get

√1681 = ± 41

Radical Form of the Square Root of 1681

The square root of 1681 in its simplest radical form is √1681. If we know the prime factorization of a number, we can write the radical form of the square root of that number. As a result, 1681’s prime factorization is 41× 41. Thus, the simplest radical form of the square root of 1681 (i.e) √41 × √41 should not be the simplest radical form.

Prime Factorization Method for the Square Root of 1681

The prime factorization method can be used to calculate the square root of 1681. To calculate the value, we must first determine the prime factorization of 1681. As a result, the prime factorization of the number 1681 is 41× 41.

Thus, √1681 = √(41× 41)

√1681 = √(41)²

√1681 = 41

As a result, the square root of 1681 equals 41.

Long Division Method for Finding the Square Root of 1681

The following are the steps for calculating the square root of 1681 using the long division method:

Step 1: First, write the number 1681. Next, pair the number 1681 by placing the bar on top of the number from right to left.

Step 2: Next, divide 16 by a number so that the multiplication of the same number is less than or equal to 16. As a result, 4×4=16, which is equal to 16. So, we get quotient = 4 and remainder = 0.

Step 3: We get 8 when we double the quotient value, so we’ll use 80 as the new divisor. Bring down the number 81 for the division process. As a result, the new dividend is 81. Determine the number such that (80 + new number)×new number gives a product that is less than or equal to 81. As a result, (80+1)×1 = 81, which is the same as 81.

Step 4: Subtract 81 from 81 to obtain 00 as the new remainder and 41 as the quotient.

Step 5: The value of the square root of 1681, √1681, is thus 41.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify the expression (10√1681) + 5

Solution:

Given: (10√1681) + 5

As we know, the square root of 1681 is 41.

Substituting the value in the expression,

(10√1681) + 5 = 10(41)+5

(10√1681) + 5 = 410 +5 = 415

Therefore, the simplification of (10√1681) + 5 is 415.

Example 2:

Find the value of m, if m√1681 – 6 = 105.

Solution:

Given: m√1681 – 6 = 105 …(1)

We know that √1681 = 41

Now, substitute the value in equation (1), we get

m(41) – 6 = 105

41m -6 = 105

41m = 105 +6 = 111

m = 111/41

m = 2.707

Therefore, the value of m is 2.707.

Example 3:

Simplify the expression: [(10√1681 × 2√1681)]/2

Solution:

Given expression:[(10√1681 × 2√1681)]/2

On cancelling square and square root, we get

Hence, the simplified form of [(10√1681 × 2√1681)]/2 is 16810.

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