Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

### Simplify Radicals

Task: Simplify the expression.

Simplifying radicals with addition/subtraction is just like combining like terms!

[tex]\[ 2 \sqrt{45} + 3 \sqrt{5} + \sqrt{12} - 6 \sqrt{3} \][/tex]

1. Combine any of the radicals that are like terms.
2. No like terms? Can you simplify any of them?
3. Now combine any of them that are similar.

Sagot :

GinnyAnswer
Let's simplify the given expression step-by-step: [tex]\(2 \sqrt{45} + 3 \sqrt{5} + \sqrt{12} - 6 \sqrt{3}\)[/tex].

### Step 1: Simplify individual square roots

First, let's simplify each radical term individually if possible.

1. [tex]\( \sqrt{45} \)[/tex]:
[tex]\[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \][/tex]

Therefore,
[tex]\[ 2 \sqrt{45} = 2 \times 3 \sqrt{5} = 6 \sqrt{5} \][/tex]

2. [tex]\( \sqrt{12} \)[/tex]:
[tex]\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \sqrt{3} \][/tex]

Therefore,
[tex]\[ \sqrt{12} = 2 \sqrt{3} \][/tex]

### Step 2: Rewrite the expression with simplified radicals

Let's substitute back the simplified radicals into the expression:

[tex]\[ 6 \sqrt{5} + 3 \sqrt{5} + 2 \sqrt{3} - 6 \sqrt{3} \][/tex]

### Step 3: Combine like terms

Now we will combine the like terms:

- Combine the [tex]\( \sqrt{5} \)[/tex] terms:
[tex]\[ 6 \sqrt{5} + 3 \sqrt{5} = (6 + 3) \sqrt{5} = 9 \sqrt{5} \][/tex]

- Combine the [tex]\( \sqrt{3} \)[/tex] terms:
[tex]\[ 2 \sqrt{3} - 6 \sqrt{3} = (2 - 6) \sqrt{3} = -4 \sqrt{3} \][/tex]

### Step 4: Write the final simplified expression

The simplified expression is:

[tex]\[ 9 \sqrt{5} - 4 \sqrt{3} \][/tex]

So, [tex]\(2 \sqrt{45} + 3 \sqrt{5} + \sqrt{12} - 6 \sqrt{3} = 9 \sqrt{5} - 4 \sqrt{3}\)[/tex].
9*root 5 - 4*root 3.
45 = 9*5
12 = 4*3
pull out 2^2 and 3^2 as coefficients
for root 5, the 3 multiplies with the 2 = 6 + 3 = 9
for root 3, the 2 is added to -6, yielding -4
add these all up and you get 9 of root 5 minus 4 of root 3, or 9*root 5 - 4*root 3
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.