Verify the Equality: 5³ - (4² + 3²) - (√100 + 8²) Step-by-Step

Question

Indicate whether the equality is true or not.

53−(42+32)−(100+82)=53−42−32−100−82 5^3-(4^2+3^2)-(\sqrt{100}+8^2)=5^3-4^2-3^2-\sqrt{100}-8^2

Video Solution

Solution Steps

00:00 Determine if the equation is correct
00:04 Calculate the exponents and root
00:33 Always solve parentheses first
00:55 Calculate the exponents and root
01:29 Continue solving according to proper order of operations from left to right
01:56 And this is the solution to the question

Step-by-Step Solution

To determine if the given equation is correct, we will simplify each of the expressions in its sides separately,

This will be done while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of these,

A. Let's start with the expression on the left side of the given equation:

53−(42+32)−(100+82) 5^3-(4^2+3^2)-(\sqrt{100}+8^2)

We'll start by simplifying the expressions inside the parentheses, we'll do this by calculating the numerical value of the terms with exponents (while remembering the definition of a root as an exponent, meaning that a root is actually an exponent), simultaneously we'll calculate the numerical value of the other terms with exponents in the expression:

53−(42+32)−(100+82)=125−(16+9)−(10+64) 5^3-(4^2+3^2)-(\sqrt{100}+8^2) =\\ 125-(16+9)-(10+64)

We'll continue and finish simplifying the expressions inside the parentheses, meaning we'll perform the addition operations in them, then we'll perform the remaining subtraction operations:

125−(16+9)−(10+64)=125−25−74=26 125-(16+9)-(10+64) =\\ 125-25-74 =\\ 26 We have finished simplifying the expression on the left side of the given equation, let's summarize the simplification steps:

53−(42+32)−(100+82)=125−25−74=26 5^3-(4^2+3^2)-(\sqrt{100}+8^2) =\\ 125-25-74 =\\ 26

B. Let's continue with simplifying the expression on the right side of the given equation:

53−42−32−100−82 5^3-4^2-3^2-\sqrt{100}-8^2

Let's remember again the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of these, and note that while this expression has no parentheses, it does have terms with exponents, so we'll start by calculating the numerical value of the terms with exponents, then we'll perform the subtraction operations:

53−42−32−100−82=125−16−9−10−64=26 5^3-4^2-3^2-\sqrt{100}-8^2= \\ 125-16-9-10-64 =\\ 26 We have finished simplifying the expression on the right side of the given equation, this simplification was brief, so there's no need to summarize,

Let's now return to the given equation and substitute in its sides the results of simplifying the expressions that were detailed in A and B:

53−(42+32)−(100+82)=53−42−32−100−82↓26=26 5^3-(4^2+3^2)-(\sqrt{100}+8^2)=5^3-4^2-3^2-\sqrt{100}-8^2 \\ \downarrow\\ 26=26

Of course this equation is indeed true, meaning - we got a true statement,

Therefore the correct answer is answer A.

Answer

True

More Questions

Related Subjects

Order of Operations: Roots Order of Operations: Exponents Order of Operations with Parentheses

Question Types

Powers and Roots: True / false Parentheses in advanced Order of Operations: True / false