Write the result of these : a. Sqrt(49)
Answers
Step-by-step explanation:
49 is a perfect square number which can be obtained by a square of 7 and it is also a composite number. Hence, the square root of 49 is a rational number. In this lesson, we will explore the concept of the square root of 49. This lesson also explains the square root of 49 in radical form along with solved examples.
Square Root of 49: √49 = 7
Square of 49: 492 = 2401
What Is the Square Root of 49?
The square root of 49 is obtained by the number whose square gives the original number.
√49 = 7
The answer obtained on squaring 7 is 49. Hence, 49 is a perfect square.
Is Square Root of 49 Rational or Irrational?
A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. We already found that √49 = 7. 7 is a whole number and it can be expressed in p/q form easily. The number 7 is a rational number. So, the square root of 49 is a rational number.
How to Find the Square Root of 49?
We will discuss two methods of finding the square root of 49
Prime Factorization
Long division
Prime factorization is a way of expressing a number as a product of its prime factors.
The prime factorization of 49 is 49 = 7 × 7
To find the square root of 49, we take one number from each pair of the same numbers and we multiply them.
49 = 7 × 7
√49 = 7
Square Root of 49 By Long Division
The value of the square root of 49 by long division method consists of the following steps:
Step 1: Starting from the right, we will pair up the digits by putting a bar above them.
Step 2: Find a number which, when multiplied to itself, gives the product less than or equal to 49. So, the number is 7. Putting the divisor as 7, we get the quotient as 7 and the remainder 0.
Step 3: The number 49 is a perfect square.
square root of 49 by long division
Explore square roots using illustrations and interactive examples
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Important Notes:
The square root is the inverse operation of squaring.
49 is a perfect square as the answer obtained after square root is a rational number.
The square root of 49 can be simplified to 7 either by using the prime factorization of 49 or by expressing 49 as a square of 7.
Challenging Questions:
We know that (-7) × (-7) =49. So, can we say that -7 is a square root of 49?
Can you determine a quadratic equation whose roots are 49 and -49?
Read More
Square Root of 49 Solved Examples
Example 1: Thomas says that the value of -(√49) is the same as (-√12). What do you think?
Solution
A negative square root cannot have real roots.
-(√49) has real roots but (-√49) has only imaginary roots.
Hence, they are not the same. -(√49) is not the same as (-√49).
Example 2: Help Ryan simplify the square root of 49 to its lowest radical form.
Solution
We need to express 49 as the product of its prime factors.
49 = 7 × 7
Therefore, √49 = 7
Thus, 7 is the lowest radical form.
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Interactive Questions
Q1.
Choose all the options that represent √49 correctly?
√7 × √7
√7 × √7
-7 × -7
-7 × -7
√(1 × 49)
√(1 × 49)
7
7
None of the above
None of the above
Q2.
Cherry is asked to mark true/false against the below-given statements. Help her mark the answers for them.
True False
Square root of 49 is irrational.
True – Square root of 49 is irrational.
False – Square root of 49 is irrational.
Square root of 49 is a whole number as it is a perfect square.
True – Square root of 49 is a whole number as it is a perfect square.
False – Square root of 49 is a whole number as it is a perfect square.
Square root of 49 is 9.
True – Square root of 49 is 9.
False – Square root of 49 is 9.
Q3.
Can you help Max match the equations with their roots.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x² - 144 = 0
x² - 49 = 0
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FAQs on Square Root of 49
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