Question

Simplify (2+ √3 ) (3+ √5)

Answer 1

Answer:

6 + 2✓5 + 3✓3 + ✓15

Step-by-step explanation:

( 2 + ✓3 ) ( 3 + ✓5 )

2 ( 3 + ✓5 ) + ✓3 ( 3 + ✓5 )

6 + 2✓5 + 3✓3 + ✓15

Hope it helps you

Answer 2

Answer:

The simplified value of $(2+\sqrt{3} )(3+\sqrt{5} )$ is $6+3\sqrt{3}+2\sqrt{5} +\sqrt{15}$.

Step-by-step explanation:

Consider the expression as follows;

$(2+\sqrt{3} )(3+\sqrt{5} )$

Recall the identity, $(a+b)(c+d)$$= ac + ad + bc + bd$

Using identity, compute the multiplication as follows:

⇒ $2(3+\sqrt{5} ) +\sqrt{3}(3+\sqrt{5} )$

⇒ $(6+2\sqrt{5} ) +(3\sqrt{3}+\sqrt{3} \sqrt{5} )$

Simplify as follows;

⇒ $(6+2\sqrt{5} ) +(3\sqrt{3}+\sqrt{15} )$ (As $\sqrt{3}\sqrt{5} = \sqrt{15}$)

Further, open up the brackets as follows:

⇒ $6+2\sqrt{5} +3\sqrt{3}+\sqrt{15}$

⇒ $6+3\sqrt{3}+2\sqrt{5} +\sqrt{15}$

Therefore, the simplified value is $6+3\sqrt{3}+2\sqrt{5} +\sqrt{15}$.

The answer implies that the product of two irrational numbers is again an irrational number but not always.

Observe that the numbers $\sqrt{3}$ and $\sqrt{5}$ are irrational numbers and 2 and 3 are rational numbers. Then $(2+\sqrt{3} )$ and $(3+\sqrt{5} )$ are also irrational numbers.

This implies the Sum of two rational and irrational number is irrational.

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