Question

Simplify 4√16 + 8√16

Simplify 7√4 x 3√8
Simplify 2√4 + 5√9
Simplify 4√5 – 2√5
Simplify -4√2 + 5√2

Answer 1

To simplify the given expressions, combine like terms by performing operations on the coefficients and only keeping the square roots.

Step-by-step explanation:

To simplify these expressions, let's first simplify each term separately and then combine like terms.

1. 4√16 = 4 × 4 = 16

2. 8√16 = 8 × 4 = 32

Therefore, 4√16 + 8√16 = 16 + 32 = 48

3. 7√4 = 7 × 2 = 14

3√8 = 3 × √4 × √2 = 3 × 2 × √2 = 6√2

Therefore, 7√4 x 3√8 = 14 × 6√2 = 84√2

4. 2√4 = 2 × 2 = 4

5√9 = 5 × 3 = 15

Therefore, 2√4 + 5√9 = 4 + 15 = 19

5. 4√5 = 4√5 = 4√5

2√5 = 2√5 = 2√5

Therefore, 4√5 – 2√5 = 4√5 - 2√5 = 0

6. -4√2 = -4√2 = -4√2

5√2 = 5√2 = 5√2

Therefore, -4√2 + 5√2 = -4√2 + 5√2 = √2

Answer 2

`4√(16) + 8√(16)`:

Since
`√(1) =1`, we get:

`4\cdot \:1\cdot \:6+8\cdot \:1\cdot \:6=24+48=72`

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`7√(4) *3√(8)`

We have
`√(4)=2`

simplify
`√(8) = √(2^3) = √(2^2*2)`

then the radical rule is used:
`\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}`

⇒
`√(2^2*2) = √(2^2) √(2)= √(4)√(2) =2√(2)`

Now we have
`√(4)=2` and
`√(8)=2 √(2)`

`7√(4) *3√(8) = 7*2*3*2√(2) = 84 √(2)`

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`2√(4)+5 √(9)`

`2√(4) =2*2= 4` and
`5√(9) =5*3= 15`

`2√(4)+5 √(9) = 4+15 = 19`

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`4√(5) -2√(5) = 2√(5)`

since
`2√(5)` is the half of
`4√(5)`

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`-4√(2)\:+\:5√(2) =1 √(2) = √(2)\\` (-4+5=1)