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Square Root of 74

The square root of 74 is expressed as √74 in the radical form and as (74)½ or (74)0.5 in the exponent form. The square root of 74 rounded up to 6 decimal places is 8.602325. It is the positive solution of the equation x2 = 74.

  • Square Root of 74: 8.602325267042627
  • Square Root of 74 in exponential form: (74)½ or (74)0.5
  • Square Root of 74 in radical form: √74
1. What Is the Square Root of 74?
2. Is Square Root of 74 Rational or Irrational?
3. How to Find the Square Root of 74?
4. Important Notes on Square Root of 74
5. FAQs on Square Root of 74
6. Challenging Questions

What is the square root of 74?

The square root of 74 is 8.602 and expressed as √74=8.6

square root of 74

 

The square root of 74 lies between the whole numbers 8 and 9

Is Square Root of 74 Rational or Irrational?

The square root of 74 is a non-terminating decimal.
√74=8.60232526704..
Also, it cannot be expressed in the form of a fraction (p/q), and hence is an irrational number.

How to Find Square Root of 74?

The square root of 74 can be easily calculated by long division.

Square root of 74 by Long Division

At each step of the long division, the quotient is added to the divisor.  Also, two digits (two zero's) are carried over in each step of the division process. The method of long division method gives an exact value of the square root. Further using this long division, the square root values of a few numbers are:

Important Notes:

  • The square root of 74 in the radical form is expressed as √74.
  • In exponent form, the square root of 74 is expressed as 74½.

Challenging Question

A school has about 744 students. On a sports meet, the teachers wish to make the students stand in columns, such that the number of students in each column is equal to the number of columns. Find the number of students in each column with the help of techniques used in square root of 74.

 

Solved Examples

 

  1. Example 1 Susan has a list of 74 guests for a party  She has to make the arrangement of chairs, such that the number of rows is equal to the number of chairs in each row.  Find the number of chairs in each row.

    Solution

    Given that Susan has 74 guests.
    Also we have:
    Number of rows = Number of chairs in each row = x
    Total chairs = Number of rows x Number of chairs in each row
    Total chairs = x × x  = x2
    We know that square root of 74 s not a perfect square. Let us try to find the number which is nearest to 74 and is a perfect square.
    The square number greater than 74 is 81
    Hence x2 = 81 = x = 9

  2.  

    Example 2 A group plans for an excursion for its members and decides to collect as much money from each member as the number of members in the group. The total amount collected is $.5476  How many members are there in the group.

    Solution

    Given that the number of members in the group is equal to the amount of money collected from each member.
    Number of member in the group = Amount collected from each member = x
    Total amount collected = $5476
    Number of members × Amount collected from each member = $5476
    x × x = 5476
    x2 = 5476
    x = √5476 = 74
    $74 is collected from each member of the group.

  3. Example: If the area of a circle is 74π in2. Find the radius of the circle.

    Solution:

    Let 'r' be the radius of the circle.
    ⇒ Area of the circle = πr2 = 74π in2
    ⇒ r = ±√74 in
    Since radius can't be negative,
    ⇒ r = √74
    The square root of 74 is 8.602.
    ⇒ r = 8.602 in

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FAQs on the Square Root of 74

What is the Value of the Square Root of 74?

The square root of 74 is 8.60232.

Why is the Square Root of 74 an Irrational Number?

Upon prime factorizing 74 i.e. 21 × 371, 2 is in odd power. Therefore, the square root of 74 is irrational.

What is the Square Root of -74?

The square root of -74 is an imaginary number. It can be written as √-74 = √-1 × √74 = i √74 = 8.602i
where i = √-1 and it is called the imaginary unit.

What is the Value of 11 square root 74?

The square root of 74 is 8.602. Therefore, 11 √74 = 11 × 8.602 = 94.626.

If the Square Root of 74 is 8.602. Find the Value of the Square Root of 0.74.

Let us represent √0.74 in p/q form i.e. √(74/100) = 0.74/10 = 0.860. Hence, the value of √0.74 = 0.860

Is the number 74 a Perfect Square?

The prime factorization of 74 = 21 × 371. Here, the prime factor 2 is not in the pair. Therefore, 74 is not a perfect square.

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