All categories

2 years ago

Simplify the expression: (2√ 27 ) ⋅ (3√ 32 )

Mathematics

2 answers:

Andrei [34K]2 years ago

8 0

<span>(2 sqrt27)*(3 sqrt32)
={2 sqrt(9*3)}*{3 sqrt(16*2)}
=(6sqrt3)*(12sqrt2)
=72 sqrt6

Hope this helps</span>

olga_2 [115]2 years ago

3 0

Remember
√(ab)=(√a)(√b)
so

simmlify each

2√27=2√(9*3)=2(√9)(√3)=2(3)(√3)=6√3
3√32=3√(16*2)=3(√16)(√2)=3(4)(√2)=12√2

so
(2√27)(3√32)=(6√3)(12√2)=(6)(√3)(√12)(√2)=(6)(12)(√3)(√2)=72√6

de answer is 72√6

You might be interested in

Prove A-(BnC) = (A-B)U(A-C), explain with an example

NikAS [45]

Answer:

Prove set equality by showing that for any element $x$ , $x \in (A \backslash (B \cap C))$ if and only if $x \in ((A \backslash B) \cup (A \backslash C))$ .

Example:

$A = \lbrace 0,\, 1,\, 2,\, 3 \rbrace$ .

$B = \lbrace0,\, 1 \rbrace$ .

$C = \lbrace0,\, 2 \rbrace$ .

$\begin{aligned} & A \backslash (B \cap C) \\ =\; & \lbrace 0,\, 1,\, 2,\, 3 \rbrace \backslash \lbrace 0 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace \end{aligned}$ .

$\begin{aligned}& (A \backslash B) \cup (A \backslash C) \\ =\; & \lbrace 2,\, 3\rbrace \cup \lbrace 1,\, 3 \rbrace \\ =\; & \lbrace 1,\, 2,\, 3 \rbrace\end{aligned}$ .

Step-by-step explanation:

Proof for $[x \in (A \backslash (B \cap C))] \implies [x \in ((A \backslash B) \cup (A \backslash C))]$ for any element $x$ :

Assume that $x \in (A \backslash (B \cap C))$ . Thus, $x \in A$ and $x \not \in (B \cap C)$ .

Since $x \not \in (B \cap C)$ , either $x \not \in B$ or $x \not \in C$ (or both.)

If $x \not \in B$ , then combined with $x \in A$ , $x \in (A \backslash B)$ .
Similarly, if $x \not \in C$ , then combined with $x \in A$ , $x \in (A \backslash C)$ .

Thus, either $x \in (A \backslash B)$ or $x \in (A \backslash C)$ (or both.)

Therefore, $x \in ((A \backslash B) \cup (A \backslash C))$ as required.

Proof for $[x \in ((A \backslash B) \cup (A \backslash C))] \implies [x \in (A \backslash (B \cap C))]$ :

Assume that $x \in ((A \backslash B) \cup (A \backslash C))$ . Thus, either $x \in (A \backslash B)$ or $x \in (A \backslash C)$ (or both.)

If $x \in (A \backslash B)$ , then $x \in A$ and $x \not \in B$ . Notice that $(x \not \in B) \implies (x \not \in (B \cap C))$ since the contrapositive of that statement, $(x \in (B \cap C)) \implies (x \in B)$ , is true. Therefore, $x \not \in (B \cap C)$ and thus $x \in A \backslash (B \cap C)$ .
Otherwise, if $x \in A \backslash C$ , then $x \in A$ and $x \not \in C$ . Similarly, $x \not \in C \!$ implies $x \not \in (B \cap C)$ . Therefore, $x \in A \backslash (B \cap C)$ .

Either way, $x \in A \backslash (B \cap C)$ .

Therefore, $x \in ((A \backslash B) \cup (A \backslash C))$ implies $x \in A \backslash (B \cap C)$ , as required.

8 0

2 years ago

HELP ME HOW DO I DO THIS I ALWAYS GET IT WRONG I NEED HELP AND NEED TO KNOW HOW YOU DID IT PLEASEEEEEEEE

seraphim [82]

Answer:

Step-by-step explanation:

The surface area of a rectangular prism has six sides so you must find the sum of the areas of all sides.

A=2xy+2xz+2yz

A=2(xy+xz+yz) you have x,y,z as 3,2,4 so

A=2(3(2)+3(4)+2(4))

A=2(6+12+8)

A=2(26)

A=52 cm^2

7 0

2 years ago

Read 2 more answers

A 44 ft ladder leans against a building so that the top of the ladder touches the building at a point 27 ft above the ground. To

Veseljchak [2.6K]

Answer is option 4. working out attached

hope it helps :)

4 0

3 years ago

A. i. Write down the 2 x 2 matrix. R, corresponding to a reflection in the origin

lisov135 [29]

Answer:

Step-by-step explanation:

that was easy

7 0

2 years ago

The area of the floor in Harmony's square bedroom is 16m2. What is the length of her bedroom

prisoha [69]

Answer:

Ask Siri.

Step-by-step explanation:

Step 1: Pull out your Iphone or sAmSUnG.

Step 2: For your Iphone hold the home button or say "hey siry..."

Step 3:(If nEeDed) For your sAmSunG go to your nearest GameStop and try to sell it at the register. They'll probably give you like 20 bucks for it b/c that is what it's worth maybe even less but whatevs... And then go and spend your college fund on a brand new Iphone and you'll be part of the Kool Kids Klub (KKK).

6 0

2 years ago

Read 2 more answers