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Square Root of 1458

The square root of 1458 is expressed as √1458 in the radical form and as (1458)^½ or (1458)^0.5 in the exponent form. The square root of 1458 rounded up to 5 decimal places is 38.18377. It is the positive solution of the equation x² = 1458. We can express the square root of 1458 in its lowest radical form as 27 √2.

Square Root of 1458: 38.18376618407357
Square Root of 1458 in exponential form: (1458)^½ or (1458)^0.5
Square Root of 1458 in radical form: √1458 or 27 √2

Square Root of 1458

1.	What is the Square Root of 1458?
2.	How to find the Square Root of 1458?
3.	Is the Square Root of 1458 Irrational?
4.	FAQs

What is the Square Root of 1458?

The square root of 1458, (or root 1458), is the number which when multiplied by itself gives the product as 1458. Therefore, the square root of 1458 = √1458 = 27 √2 = 38.18376618407357.

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How to Find Square Root of 1458?

Square Root of 1458 by Long Division Method

Value of √1458 by Long Division Method

Explanation:

Forming pairs: 14 and 58
Find a number Y (3) such that whose square is <= 14. Now divide 14 by 3 with quotient as 3.
Bring down the next pair 58, to the right of the remainder 5. The new dividend is now 558.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 8) such that 6Z × Z <= 558. After finding Z, together 6 and Z (8) form a new divisor 68 for the new dividend 558.
Divide 558 by 68 with the quotient as 8, giving the remainder = 558 - 68 × 8 = 558 - 544 = 14.
Now, let's find the decimal places after the quotient 38.
Bring down 00 to the right of this remainder 14. The new dividend is now 1400.
Add the last digit of quotient to divisor i.e. 8 + 68 = 76. To the right of 76, find a digit Z (which is 1) such that 76Z × Z <= 1400. Together they form a new divisor (761) for the new dividend (1400).
Divide 1400 by 761 with the quotient as 1, giving the remainder = 1400 - 761 × 1 = 1400 - 761 = 639.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 1458.

Therefore, the square root of 1458 by long division method is 38.1 approx.

Is Square Root of 1458 Irrational?

The actual value of √1458 is undetermined. The value of √1458 up to 25 decimal places is 38.18376618407356631764560. Hence, the square root of 1458 is an irrational number.

☛ Also Check:

Square Root of 85 - √85 = 9.21954
Square Root of 1296 - √1296 = 36
Square Root of 192 - √192 = 13.85641
Square Root of 61 - √61 = 7.81025
Square Root of 361 - √361 = 19
Square Root of 90 - √90 = 9.48683
Square Root of 1681 - √1681 = 41

Square Root of 1458 Solved Examples

Example 1: Solve the equation x² − 1458 = 0

Solution:

x² - 1458 = 0 i.e. x² = 1458
x = ±√1458
Since the value of the square root of 1458 is 38.184,
⇒ x = +√1458 or -√1458 = 38.184 or -38.184.
Example 2: If the surface area of a cube is 8748 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 8748 in²
⇒ a = ±√1458 in
Since length can't be negative,
⇒ a = √1458
We know that the square root of 1458 is 38.184.
⇒ a = 38.184 in
Example 3: If the area of an equilateral triangle is 1458√3 in². Find the length of one of the sides of the triangle.

Solution:

Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a² = 1458√3 in²
⇒ a = ±√5832 in
Since length can't be negative,
⇒ a = √5832 = 2 √1458
We know that the square root of 1458 is 38.184.
⇒ a = 76.368 in

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FAQs on the Square Root of 1458

What is the Value of the Square Root of 1458?

The square root of 1458 is 38.18376.

Why is the Square Root of 1458 an Irrational Number?

Upon prime factorizing 1458 i.e. 2¹ × 3⁶, 2 is in odd power. Therefore, the square root of 1458 is irrational.

What is the Square Root of 1458 in Simplest Radical Form?

We need to express 1458 as the product of its prime factors i.e. 1458 = 2 × 3 × 3 × 3 × 3 × 3 × 3. Therefore, √1458 = √2 × 3 × 3 × 3 × 3 × 3 × 3 = 27 √2. Thus, the square root of 1458 in the lowest radical form is 27 √2.

What is the Value of 5 square root 1458?

The square root of 1458 is 38.184. Therefore, 5 √1458 = 5 × 38.184 = 190.919.

What is the Square of the Square Root of 1458?

The square of the square root of 1458 is the number 1458 itself i.e. (√1458)² = (1458)^2/2 = 1458.

Is the number 1458 a Perfect Square?

The prime factorization of 1458 = 2¹ × 3⁶. Here, the prime factor 2 is not in the pair. Therefore, 1458 is not a perfect square.

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