Simplify the following expressions: 2. sqrt(45) sqrt(27) 3. sqrt(28) sqrt(8) * sqrt(12)

Question

ScanSolve AI Tutor · Accepted Answer

The image shows an equation involving surds: $3\sqrt{5} = 2\sqrt{5} + \sqrt{5}$ . We need to verify if this equation is true by simplifying the right-hand side.

Identify the terms on the right-hand side.
The right-hand side (RHS) of the equation is $2\sqrt{5} + \sqrt{5}$ .
Combine the like surds.
Since both terms have $\sqrt{5}$ as the radical part, they are like surds and can be added by combining their coefficients.
$2\sqrt{5} + \sqrt{5} = (2+1)\sqrt{5}$
Simplify the expression.
$(2+1)\sqrt{5} = 3\sqrt{5}$
Compare with the left-hand side.
The left-hand side (LHS) of the equation is $3\sqrt{5}$ .
Since the simplified RHS ( $3\sqrt{5}$ ) is equal to the LHS ( $3\sqrt{5}$ ), the equation is true.
$\boxed{3\sqrt{5} = 3\sqrt{5}}$

Simplify the following expressions: 2. sqrt(45) sqrt(27) 3. sqrt(28) sqrt(8) * sqrt(12)

Step-by-step solution

Identify the terms on the right-hand side.

Combine the like surds.

Simplify the expression.

Compare with the left-hand side.

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