/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 45 Solve. $$\sqrt{b+3}-2=1$$... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 45

Solve. $$\sqrt{b+3}-2=1$$

Short Answer

Expert verified
The solution is b = 6.

Step by step solution

01

Isolate the square root

To start, add 2 to both sides of the equation to isolate the square root term.$$ \ \sqrt{b+3} - 2 + 2 = 1 + 2 \ \sqrt{b+3} = 3 $$
02

Square both sides of the equation

Square both sides to remove the square root. $$ \ (\sqrt{b+3})^2 = 3^2 \ b + 3 = 9 $$
03

Solve for b

Subtract 3 from both sides to solve for b. $$ \ b + 3 - 3 = 9 - 3 \ b = 6 $$
04

Verify the solution

Double-check the solution by substituting back into the original equation.$$ \ \sqrt{b+3} - 2 = 1$$ \ \sqrt{6+3} - 2 = 1 \ \sqrt{9} - 2 = 1 \ 3 - 2 = 1 \ 1 = 1 $$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Isolating the Radical
When solving radical equations, the first goal is to isolate the radical expression. To achieve this, you move all other terms to the opposite side of the equation. For example, consider the equation: \text{ } \text{\text{$$\text{\text{\text{$$\text{\text{\text{\text{\text{($$\text{\text{\text{\text{\text{\text{\text{\text{($$\text{\text{\text{\text{\text{$$\text{\text{\text{\text{\text{($$\text{\text{\text{\text{\text{($$\text{\text{\text{\text{\text{\text{\flow lines. Instead, you want to isolate \text{ewline}{}In this case, we'll add 2 to both sides to achieve this, as follows:\text{ewline{}ewfind it useful锟�, thisstep clear so it's easier to proceed. \text{ewline}ew }ewline } \text{\text{\text \(\text{\)\text{\( ewline )=3\)}\() 3TextCto fill}} }} }, \textengthe root term by manipulating the equation appropriately makes all subsequent steps straightforward.ewline \text{ewline it easier to proceed.equationproceedspland.$$ewline \) before. ewline proceed.ewline$$ to}}ewlineevery.$$'equation.

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Most popular questions from this chapter

Solve and write interval notation for the solution set. Then graph the solution set. $$|2 x+1|>-\frac{1}{2}$$

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