What is the smallest number by which 336 be divided so that the quotient is a perfect square?

Solution:

(i) 402

We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 2. Therefore 2 must be subtracted from 402 to get a perfect square.

\therefore402-2=400

Hence, the square root of 400 is 20.

(ii) 1989

We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 53. Therefore 53must be subtracted from 1989 to get a perfect square.

\therefore1989-53=1936

Hence, the square root of 1936 is 44.

(iii) 3250

We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 1. Therefore 1 must be subtracted from 3250 to get a perfect square.

\therefore3250-1=3249

Hence, the square root of 3249 is 57.

(iv) 825

We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get remainder 41. Therefore 41 must be subtracted from 825 to get a perfect square.

\therefore825-41=784

Hence, the square root of 784 is 28.

(v) 4000

We know that, if we subtract the remainder from the number, we get a perfect square.

Here, we get the remainder 31. Therefore 31 must be subtracted from 4000 to get a perfect square.

\therefore4000-31=3969

Hence, the square root of 3969 is 63.

The square root of 336 is expressed as √336 in the radical form and as (336)½ or (336)0.5 in the exponent form. The square root of 336 rounded up to 9 decimal places is 18.330302780. It is the positive solution of the equation x2 = 336. We can express the square root of 336 in its lowest radical form as 4 √21.

• Square Root of 336: 18.33030277982336
• Square Root of 336 in exponential form: (336)½ or (336)0.5
• Square Root of 336 in radical form: √336 or 4 √21

The square root of 336, (or root 336), is the number which when multiplied by itself gives the product as 336. Therefore, the square root of 336 = √336 = 4 √21 = 18.33030277982336.

☛ Check: Square Root Calculator

Value of √336 by Long Division Method

Explanation:

• Forming pairs: 03 and 36
• Find a number Y (1) such that whose square is <= 3. Now divide 03 by 1 with quotient as 1.
• Bring down the next pair 36, to the right of the remainder 2. The new dividend is now 236.
• Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 8) such that 2Z × Z <= 236. After finding Z, together 2 and Z (8) form a new divisor 28 for the new dividend 236.
• Divide 236 by 28 with the quotient as 8, giving the remainder = 236 - 28 × 8 = 236 - 224 = 12.
• Now, let's find the decimal places after the quotient 18.
• Bring down 00 to the right of this remainder 12. The new dividend is now 1200.
• Add the last digit of quotient to divisor i.e. 8 + 28 = 36. To the right of 36, find a digit Z (which is 3) such that 36Z × Z <= 1200. Together they form a new divisor (363) for the new dividend (1200).
• Divide 1200 by 363 with the quotient as 3, giving the remainder = 1200 - 363 × 3 = 1200 - 1089 = 111.
• Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 336.

Therefore, the square root of 336 by long division method is 18.3 approximately.

The actual value of √336 is undetermined. The value of √336 up to 25 decimal places is 18.33030277982336002635219. Hence, the square root of 336 is an irrational number.

☛ Also Check:

1. Example 1: Solve the equation x2 − 336 = 0

   Solution:

   x2 - 336 = 0 i.e. x2 = 336 x = ±√336 Since the value of the square root of 336 is 18.330,

   ⇒ x = +√336 or -√336 = 18.330 or -18.330.

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The square root of 336 is 18.3303.

Why is the Square Root of 336 an Irrational Number?

Upon prime factorizing 336 i.e. 24 × 31 × 71, 3 is in odd power. Therefore, the square root of 336 is irrational.

Evaluate 16 plus 10 square root 336

The given expression is 16 + 10 √336. We know that the square root of 336 is 18.330. Therefore, 16 + 10 √336 = 16 + 10 × 18.330 = 16 + 183.303 = 199.303

What is the Square Root of 336 in Simplest Radical Form?

We need to express 336 as the product of its prime factors i.e. 336 = 2 × 2 × 2 × 2 × 3 × 7. Therefore, √336 = √2 × 2 × 2 × 2 × 3 × 7 = 4 √21. Thus, the square root of 336 in the lowest radical form is 4 √21.

What is the Square of the Square Root of 336?

The square of the square root of 336 is the number 336 itself i.e. (√336)2 = (336)2/2 = 336.

What is the Value of 20 square root 336?

The square root of 336 is 18.330. Therefore, 20 √336 = 20 × 18.330 = 366.606.

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