Solve (√9 - √4)² × 4² - 5: Complete Square Root Operation

Question

Calculate and indicate the answer:

(9−4)2⋅42−51 (\sqrt{9}-\sqrt{4})^2\cdot4^2-5^1

Video Solution

Solution Steps

00:00 Solve
00:03 Always solve roots and exponents first
00:11 Solve the parentheses
00:20 1 raised to any power is always equal to 1
00:25 An exponent is the number multiplied by itself as many times as the power indicates
00:28 Calculate the exponents and then substitute in our exercise
00:30 Any number (A) raised to the power of 1 is always equal to the number itself (A)
00:36 Continue to solve multiplication and division before addition and subtraction
00:40 And this is the solution to the question

Step-by-Step Solution

Previously mentioned in the order of operations that exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate then first the value of the expression inside the parentheses (by calculating the roots inside the parentheses first) :

(9−4)2⋅42−51=(3−2)2⋅42−51=12⋅42−51 (\sqrt{9}-\sqrt{4})^2\cdot4^2-5^1 =(3-2)^2\cdot4^2-5^1 =1^2\cdot4^2-5^1 where in the second stage we simplified the expression in parentheses,

Next we'll calculate the values of the terms with exponents:

12⋅42−51=1⋅16−5 1^2\cdot4^2-5^1 =1\cdot16-5 then we'll calculate the results of the multiplications

1⋅16−5=16−5 1\cdot16-5 =16-5 and after that we'll perform the subtraction:

16−5=11 16-5=11 Therefore the correct answer is answer B.

Answer

11

More Questions

Related Subjects

The Order of Operations Order of Operations: Roots Order of Operations: Exponents Order or Hierarchy of Operations with Fractions

Question Types

Powers and Roots: Using parentheses