Respuesta :
Hello! The square root of 121 is just 11. Since 11^2 is 121. Because this is a whole number, it is rational. The square root of 48 can be factored out to 16 and 3. Because 16 x 3 is 48. You can take the square root of 16, which is 4. So, the square root of 48 is 4 root 3 (since you can’t square root 3 anymore it is stuck inside the square root). Because there is still a number you can’t square root anymore stuck in the root, the answer is irrational. Any number like, square root 2, square root 5, is irrational. So, square root of 121=11 which is rational, and square root of 48= 4*square root of 3 which is irrational. :)
Answer:
[tex] \sqrt{121} = 11 [/tex] (rational)
[tex] \sqrt{48} = 4\sqrt{3} [/tex] (irrational)
Step-by-step explanation:
To simplify each square root expression and determine whether the simplified form is rational or irrational, let's solve the given problems step by step.
1. Square Root of 121
To find the square root of [tex]121[/tex], we use the property that [tex]\sqrt{a^2} = a[/tex] for [tex]a \geq 0[/tex]. Here, [tex]121[/tex] is a perfect square.
[tex] \sqrt{121} = \sqrt{11^2}= 11 [/tex]
Therefore, the simplified form of [tex]\sqrt{121}[/tex] is [tex] \boxed{11} [/tex], which is a rational number because [tex]11[/tex] is an integer.
2. Square Root of 48
To simplify [tex]\sqrt{48}[/tex], we can break it down into its prime factors and then use properties of square roots.
[tex] \sqrt{48} = \sqrt{16 \times 3} [/tex]
Notice that [tex]16[/tex] is a perfect square ([tex]4^2[/tex]). Therefore,
[tex] \sqrt{48} = \sqrt{16 \times 3}\\\\ = \sqrt{16} \times \sqrt{3} \\\\ = \sqrt{4^2} \times \sqrt{3} \\\\= 4 \times \sqrt{3} [/tex]
So, [tex]\sqrt{48}[/tex] simplifies to [tex] \boxed{4\sqrt{3}} [/tex], which is an irrational number because [tex]\sqrt{3}[/tex] is not a rational number (it is not the ratio of two integers).
Therefore:
[tex] \sqrt{121} = 11 [/tex] (rational)
[tex] \sqrt{48} = 4\sqrt{3} [/tex] (irrational)
These are the simplified forms of the given square root expressions along with their descriptions as rational or irrational numbers.
